bluuebunny/crossref_metadata_2025 huggingface dataset:
Combinatorial Interpretations of the Kreweras Triangle in Terms of Subset Tuples
Authors: Bigeni Ange
Published: January 2020

We show how the combinatorial interpretation of the normalized median Genocchi numbers in terms of multiset tuples, defined by Hetyei in his study of the alternation acyclic tournaments, is bijectively equivalent to previous models like the normalized Dumont permutations or the Dellac configurations, and we extend the interpretation to the Kreweras triangle.
Hultman Elements for the Hyperoctahedral Groups
Authors: Woo Alexander
Published: January 2020

Hultman, Linusson, Shareshian, and Sjöstrand gave a pattern avoidance characterization of the permutations for which the number of chambers of its associated inversion arrangement is the same as the size of its lower interval in Bruhat order. Hultman later gave a characterization, valid for an arbitrary finite reflection group, in terms of distances in the Bruhat graph. On the other hand, the pattern avoidance criterion for permutations had earlier appeared in independent work of Sjöstrand and of Gasharov and Reiner. We give characterizations of the elements of the hyperoctahedral groups satisfying Hultman's criterion that is in the spirit of those of Sjöstrand and of Gasharov and Reiner. We also give a pattern avoidance criterion using the notion of pattern avoidance defined by Billey and Postnikov.
The IC-Indices of Complete Bipartite Graphs
Authors: Shiue Chin-Lin , Fu Hung-Lin
Published: January 2020

Let $G$ be a connected graph, and let $f$ be a function mapping $V(G)$ into ${\Bbb N}$. We define $f(H)=\sum_{v\in{V(H)}}f(v)$ for each subgraph $H$ of $G$. The function $f$ is called an IC-coloring of $G$ if for each integer $k$ in the set $\{1,2,\cdots,f(G)\}$ there exists an (induced) connected subgraph $H$ of $G$ such that $f(H)=k$, and the IC-index of $G$, $M(G)$, is the maximum value of $f(G)$ where $f$ is an IC-coloring of $G$. In this paper, we show that $M(K_{m,n})=3\cdot2^{m+n-2}-2^{m-2}+2$ for each complete bipartite graph $K_{m,n},\,2\leq m\leq n$.
On the Turán Properties of Infinite Graphs
Authors: Dudek Andrzej , Rödl Vojtěch
Published: January 2020

Let $G^{(\infty)}$ be an infinite graph with the vertex set corresponding to the set of positive integers ${\Bbb N}$. Denote by $G^{(l)}$ a subgraph of $G^{(\infty)}$ which is spanned by the vertices $\{1,\dots,l\}$. As a possible extension of Turán's theorem to infinite graphs, in this paper we will examine how large $\liminf_{l\rightarrow \infty} {|E(G^{(l)})|\over l^2}$ can be for an infinite graph $G^{(\infty)}$, which does not contain an increasing path $I_k$ with $k+1$ vertices. We will show that for sufficiently large $k$ there are $I_k$–free infinite graphs with ${1\over 4}+{1\over 200} < \liminf_{l\rightarrow \infty} {|E(G^{(l)})|\over l^2}$. This disproves a conjecture of J. Czipszer, P. Erdős and A. Hajnal. On the other hand, we will show that $\liminf_{l\rightarrow \infty} {|E(G^{(l)})|\over l^2}\le{1\over 3}$ for any $k$ and such $G^{(\infty)}$.
The Lonely Runner with Seven Runners
Authors: Barajas J. , Serra O.
Published: January 2020

Suppose $k+1$ runners having nonzero constant pairwise distinct speeds run laps on a unit-length circular track starting at the same time and place. A runner is said to be lonely if she is at distance at least $1/(k+1)$ along the track to every other runner. The lonely runner conjecture states that every runner gets lonely. The conjecture has been proved up to six runners ($k\le 5$). A formulation of the problem is related to the regular chromatic number of distance graphs. We use a new tool developed in this context to solve the first open case of the conjecture with seven runners.
Polynomiality of Certain Average Weights for Oscillating Tableaux
Authors: Han Guo-Niu , Xiong Huan
Published: January 2020

We prove that a family of average weights for oscillating tableaux are polynomials in two variables, namely, the length of the oscillating tableau and the size of the ending partition, which generalizes a result of Hopkins and Zhang. Several explicit and asymptotic formulas for the average weights are also derived. The main idea in this paper is to translate the study of certain average weights for oscillating tableaux to the study of an operator $\Psi$ from the set of real coefficient polynomials with two parameters to itself.
Cyclic Triangle Factors in Regular Tournaments
Authors: Li Lina , Molla Theodore
Published: January 2020

Both Cuckler and Yuster independently conjectured that when $n$ is an odd positive multiple of $3$ every regular tournament on $n$ vertices contains a collection of $n/3$ vertex-disjoint copies of the cyclic triangle. Soon after, Keevash \& Sudakov proved that if $G$ is an orientation of a graph on $n$ vertices in which every vertex has both indegree and outdegree at least $(1/2 - o(1))n$, then there exists a collection of vertex-disjoint cyclic triangles that covers all but at most $3$ vertices. In this paper, we resolve the conjecture of Cuckler and Yuster for sufficiently large $n$.
On the Diameter of Tree Associahedra
Authors: Cardinal Jean , Langerman Stefan , Pérez-Lantero Pablo
Published: January 2020

We consider a natural notion of search trees on graphs, which we show is ubiquitous in various areas of discrete mathematics and computer science. Search trees on graphs can be modified by local operations called rotations, which generalize rotations in binary search trees. The rotation graph of search trees on a graph $G$ is the skeleton of a polytope called the graph associahedron of $G$.We consider the case where the graph $G$ is a tree. We construct a family of trees $G$ on $n$ vertices and pairs of search trees on $G$ such that the minimum number of rotations required to transform one search tree into the other is $\Omega (n\log n)$. This implies that the worst-case diameter of tree associahedra is $\Theta (n\log n)$, which answers a question from Thibault Manneville and Vincent Pilaud. The proof relies on a notion of projection of a search tree which may be of independent interest.
Polyhedra with Few 3-Cuts are Hamiltonian
Authors: Brinkmann G. , Zamfirescu C. T.
Published: January 2020

In 1956, Tutte showed that every planar 4-connected graph is hamiltonian. In this article, we will generalize this result and prove that polyhedra with at most three $3$-cuts are hamiltonian. In 2002 Jackson and Yu have shown this result for the subclass of triangulations. We also prove that polyhedra with at most four $3$-cuts have a hamiltonian path. It is well known that for each $k\ge 6$ non-hamiltonian polyhedra with $k$ $3$-cuts exist. We give computational results on lower bounds on the order of a possible non-hamiltonian polyhedron for the remaining open cases of polyhedra with four or five $3$-cuts.
Ehrhart Polynomial Roots of Reflexive Polytopes
Authors: Hegedüs Gábor , Higashitani Akihiro , Kasprzyk Alexander
Published: January 2020

Recent work has focused on the roots $z\in\mathbb{C}$ of the Ehrhart polynomial of a lattice polytope $P$. The case when $\Re{z}=-1/2$ is of particular interest: these polytopes satisfy Golyshev's "canonical line hypothesis". We characterise such polytopes when $\mathrm{dim}(P)\leq 7$. We also consider the "half-strip condition", where all roots $z$ satisfy $-\mathrm{dim}(P)/2\leq\Re{z}\leq \mathrm{dim}(P)/2-1$, and show that this holds for any reflexive polytope with $\mathrm{dim}(P)\leq 5$. We give an example of a $10$-dimensional reflexive polytope which violates the half-strip condition, thus improving on an example by Ohsugi–Shibata in dimension $34$.
Vertically Constrained Motzkin-Like Paths Inspired by Bobbin Lace
Authors: Irvine Veronika , Melczer Stephen , Ruskey Frank
Published: January 2020

Inspired by a new mathematical model for bobbin lace, this paper considers finite lattice paths formed from the set of step vectors $\mathfrak{A}=$$\{\rightarrow,$ $\nearrow,$ $\searrow,$ $\uparrow,$ $\downarrow\}$ with the restriction that vertical steps $(\uparrow, \downarrow)$ cannot be consecutive. The set $\mathfrak{A}$ is the union of the well known Motzkin step vectors $\mathfrak{M}=$$\{\rightarrow,$ $\nearrow,$ $\searrow\}$ with the vertical steps $\{\uparrow, \downarrow\}$. An explicit bijection $\phi$ between the exhaustive set of vertically constrained paths formed from $\mathfrak{A}$ and a bisection of the paths generated by $\mathfrak{M}S$ is presented. In a similar manner, paths with the step vectors $\mathfrak{B}=$$\{\nearrow,$ $\searrow,$ $\uparrow,$ $\downarrow\}$, the union of Dyck step vectors and constrained vertical steps, are examined.  We show, using the same $\phi$ mapping, that there is a bijection between vertically constrained $\mathfrak{B}$ paths and the subset of Motzkin paths avoiding horizontal steps at even indices.  Generating functions are derived to enumerate these vertically constrained, partially directed paths when restricted to the half and quarter-plane.  Finally, we extend Schröder and Delannoy step sets in a similar manner and find a bijection between these paths and a subset of Schröder paths that are smooth (do not change direction) at a regular horizontal interval.
A Quantified Version of Bourgain's Sum-Product Estimate in ${\Bbb F}_p$ for Subsets of Incomparable Sizes
Authors: Garaev M. Z.
Published: January 2020

Let ${\Bbb F}_p$ be the field of residue classes modulo a prime number $p.$ In this paper we prove that if $A,B\subset {\Bbb F}_p^*,$ then for any fixed $\varepsilon>0,$ $$ |A+A|+|AB|\gg \Bigl(\min\Bigl\{|B|,\, {p\over|A|}\Bigr\}\Bigr)^{1/25-\varepsilon}|A|. $$ This quantifies Bourgain's recent sum-product estimate.
On a Conjecture Regarding Identification in Hamming Graphs
Authors: Junnila Ville , Laihonen Tero , Lehtilä Tuomo
Published: January 2020

In 2013, Goddard and Wash studied identifying codes in the Hamming graphs $K_q^n$. They stated, for instance, that $\gamma^{ID}(K_q^n)\leqslant q^{n-1}$ for any $q$ and $n\geqslant 3$. Moreover, they conjectured that $\gamma^{ID}(K_q^3)=q^2$. In this article, we show that $\gamma^{ID}(K_q^3)\leqslant q^2-q/4$ when $q$ is a power of four, which disproves the conjecture. Goddard and Wash also gave the lower bound $\gamma^{ID}(K_q^3)\geqslant q^2-q\sqrt{q}$. We improve this bound to $\gamma^{ID}(K_q^3)\geqslant q^2-\frac{3}{2} q$. Moreover, we improve the above mentioned bound $\gamma^{ID}(K_q^n)\leqslant q^{n-1}$ to $\gamma^{ID}(K_q^n)\leqslant q^{n-k}$ for $n=3\frac{q^k-1}{q-1}$ and to $\gamma^{ID}(K_q^n)\leqslant 3q^{n-k}$ for $n=\frac{q^k-1}{q-1}$, when $q$ is a prime power. For these bounds, we utilize two classes of closely related codes, namely, the self-identifying and the self-locating-dominating codes. In addition, we show that the self-locating-dominating codes satisfy the result $\gamma^{SLD}(K_q^3)=q^2$ related to the above conjecture.
An Explicit Edge-Coloring of $K_n$ with Six Colors on Every $K_5$
Authors: Cameron Alex
Published: January 2020

Let $p$ and $q$ be positive integers such that $1 \leq q \leq {p \choose 2}$. A $(p,q)$-coloring of the complete graph on $n$ vertices $K_n$ is an edge coloring for which every $p$-clique contains edges of at least $q$ distinct colors. We denote the minimum number of colors needed for such a $(p,q)$-coloring of $K_n$ by $f(n,p,q)$. This is known as the Erdös-Gyárfás function. In this paper we give an explicit $(5,6)$-coloring with $n^{1/2+o(1)}$ colors. This improves the best known upper bound of $f(n,5,6)=O\left(n^{3/5}\right)$ given by Erdös and Gyárfás, and comes close to matching the order of the best known lower bound, $f(n,5,6) = \Omega\left(n^{1/2}\right)$.
On the Subnet Prune and Regraft Distance
Authors: Klawitter Jonathan , Linz Simone
Published: January 2020

Phylogenetic networks are rooted directed acyclic graphs that represent evolutionary relationships between species whose past includes reticulation events such as hybridisation and horizontal gene transfer. To search the space of phylogenetic networks, the popular tree rearrangement operation rooted subtree prune and regraft (rSPR) was recently generalised to phylogenetic networks. This new operation – called subnet prune and regraft (SNPR) – induces a metric on the space of all phylogenetic networks as well as on several widely-used network classes. In this paper, we investigate several problems that arise in the context of computing the SNPR-distance. For a phylogenetic tree $T$ and a phylogenetic network $N$, we show how this distance can be computed by considering the set of trees that are embedded in $N$ and then use this result to characterise the SNPR-distance between $T$ and $N$ in terms of agreement forests. Furthermore, we analyse properties of shortest SNPR-sequences between two phylogenetic networks $N$ and $N'$, and answer the question whether or not any of the classes of tree-child, reticulation-visible, or tree-based networks isometrically embeds into the class of all phylogenetic networks under SNPR.
Flip Posets of Bruhat Intervals
Authors: Blanco Saúl A.
Published: January 2020

In this paper we introduce a way of partitioning the paths of shortest lengths in the Bruhat graph $B(u,v)$ of a Bruhat interval $[u,v]$ into rank posets $P_{i}$ in a way that each $P_{i}$ has a unique maximal chain that is rising under a reflection order. In the case where each $P_{i}$ has rank three, the construction yields a combinatorial description of some terms of the complete $\textbf{cd}$-index as a sum of ordinary $\textbf{cd}$-indices of Eulerian posets obtained from each of the $P_{i}$.
Shuffle-Compatible Permutation Statistics II: The Exterior Peak Set
Authors: Grinberg Darij
Published: January 2020

This paper is a continuation of the work "Shuffle-compatible permutation statistics" by Gessel and Zhuang (but can be read independently from the latter). We study the shuffle-compatibility of permutation statistics — a concept introduced by Gessel and Zhuang, although various instances of it have appeared throughout the literature before. We prove that (as Gessel and Zhuang have conjectured) the exterior peak set statistic (Epk) is shuffle-compatible. We furthermore introduce the concept of an "LR-shuffle-compatible" statistic, which is stronger than shuffle-compatibility. We prove that Epk and a few other statistics are LR-shuffle-compatible. Furthermore, we connect these concepts with the quasisymmetric functions, in particular the dendriform structure on them.
Random Kneser Graphs and Hypergraphs
Authors: Kupavskii Andrey
Published: January 2020

The Kneser graph $KG_{n,k}$ is the graph whose vertices are the $k$-element subsets of $[n],$ with two vertices adjacent if and only if the corresponding sets are disjoint. A famous result due to Lovász states that the chromatic number of $KG_{n,k}$ is equal to $n-2k+2$. In this paper we discuss the chromatic number of random Kneser graphs and hypergraphs. It was studied in two recent papers, one due to Kupavskii, who proposed the problem and studied  the graph case, and the more recent one due to Alishahi and Hajiabolhassan. The authors of the latter paper had extended the result of Kupavskii to the case of general Kneser hypergraphs. Moreover, they have improved the bounds of Kupavskii in the graph case for many values of parameters.In the present paper we present a purely combinatorial approach to the problem based on blow-ups of graphs, which gives much better bounds on the chromatic number of random Kneser and Schrijver graphs and Kneser hypergraphs. This allows us to improve all known results on the topic. The most interesting improvements are obtained in the case of $r$-uniform Kneser hypergraphs with $r\ge 3$, where we managed to replace certain polynomial dependencies of the parameters by the logarithmic ones.
Graph Families with Constant Distance Determinant
Authors: Cheng Yen-Jen , Lin Jephian C.-H.
Published: January 2020

This paper introduces a new class of graphs, the clique paths (or the CP graphs), and shows that their distance determinant and distance inertia are independent of their structures. The CP graphs include the family of linear $2$-trees. When a graph is attached to a CP graph, it is shown that the distance determinant and the distance inertia are also independent of the structure of the CP graph. Applications to the addressing problem proposed by Graham and Pollak in 1971 are given.
Total Distance, Wiener Index and Opportunity Index in Wreath Products of Star Graphs
Authors: Cavaleri Matteo , Donno Alfredo , Scozzari Andrea
Published: January 2020

In the last decades much attention has turned towards centrality measures on graphs. The Wiener index and the total distance are key tools to investigate the median vertices, the distance-balanced property and the opportunity index of a graph. This interest has recently been addressed to graphs obtained via classical graph products like the Cartesian, the direct, the strong and the lexicographic product. We extend this study to a relatively new graph product, that is, the wreath product. In this paper, we compute the total distance for the vertices of an arbitrary wreath product graph $G\wr H$ in terms of the total distances in $H$ and of some distance-based indices of $G$. We explicitly compute these indices for the star graph $S_n$, providing a closed formula for the total distances in $S_n\wr H$ when $H$ is complete or a star. As a consequence, we obtain the Wiener index of these graphs, we characterize the median and the central vertices, and finally we give an upper and a lower bound for the opportunity index of $S_n\wr S_m$ in terms of tail conditional expectations of an associated binomial distribution.
The Classification of $2$-Extendable Edge-Regular Graphs with Diameter $2$
Authors: Kutnar Klavdija , Marušič Dragan , Miklavič Štefko , Šparl Primož
Published: January 2020

Let $\ell$ denote a non-negative integer. A connected graph $\Gamma$ of even order at least $2\ell+2$ is $\ell$-extendable if it contains a matching of size $\ell$ and if every such matching is contained in a perfect matching of $\Gamma$. A connected regular graph $\Gamma$ is edge-regular, if there exists an integer $\lambda$ such that every pair of adjacent vertices of $\Gamma$ have exactly $\lambda$  common neighbours. In this paper we classify $2$-extendable edge-regular graphs of even order and diameter $2$.
Products of Factorial Schur Functions
Authors: Kreiman Victor
Published: January 2020

The product of any finite number of factorial Schur functions can be expanded as a ${\Bbb Z}[{\bf y}]$-linear combination of Schur functions. We give a rule for computing the coefficients in such an expansion. This rule generalizes the classical Littlewood-Richardson rule and several special cases of the Molev-Sagan rule.
Saturation Games for Odd Cycles
Authors: Spiro Sam
Published: January 2020

Given a family of graphs $\mathcal{F}$, we consider the $\mathcal{F}$-saturation game.  In this game, two players alternate adding edges to an initially empty graph on $n$ vertices, with the only constraint being that neither player can add an edge that creates a subgraph that lies in $\mathcal{F}$.  The game ends when no more edges can be added to the graph.  One of the players wishes to end the game as quickly as possible, while the other wishes to prolong the game.  We let $\textrm{sat}_g(\mathcal{F};n)$ denote the number of edges that are in the final graph when both players play optimally.

The $\{C_3\}$-saturation game was the first saturation game to be considered, but as of now the order of magnitude of $\textrm{sat}_g(\{C_3\},n)$ remains unknown.  We consider a variation of this game.  Let $\mathcal{C}_{2k+1}:=\{C_3,\ C_5,\ldots,C_{2k+1}\}$. We prove that $\textrm{sat}_g(\mathcal{C}_{2k+1};n)\ge(\frac{1}{4}-\epsilon_k)n^2+o(n^2)$ for all $k\ge 2$ and that $\textrm{sat}_g(\mathcal{C}_{2k+1};n)\le (\frac{1}{4}-\epsilon'_k)n^2+o(n^2)$ for all $k\ge 4$, with $\epsilon_k<\frac{1}{4}$ and $\epsilon'_k>0$ constants tending to 0 as $k\to \infty$.  In addition to this we prove $\textrm{sat}_g(\{C_{2k+1}\};n)\le \frac{4}{27}n^2+o(n^2)$ for all $k\ge 2$, and $\textrm{sat}_g(\mathcal{C}_\infty\setminus C_3;n)\le 2n-2$, where $\mathcal{C}_\infty$ denotes the set of all odd cycles.
Totally Greedy Coin Sets and Greedy Obstructions
Authors: Cowen L. J. , Cowen Robert , Steinberg Arthur
Published: January 2020

A coin set is a strictly increasing list of positive integers that always begins with 1. A coin set is called greedy when the simple greedy change-making algorithm always produces the fewest number of coins in change. Here, the greedy change-making algorithm repeatedly selects the largest denomination coin less than the remaining amount until it has assembled the correct change. Pearson has provided an efficient algorithm for determining whether a coin set is greedy. We study a stricter property on coin sets, called total greediness, which requires that all initial subsequences of the coin set also be greedy, and a simple property makes it easy to test if a coin set is totally greedy. We begin to explore the theory of greedy obstructions– those coin sets that cannot be extended to greedy coin sets by the addition of coins in larger denominations.
On a Positivity Conjecture in the Character Table of $S_n$
Authors: Sundaram Sheila
Published: January 2020

In previous work of this author it was conjectured that the sum of power sums $p_\lambda,$ for partitions $\lambda$ ranging over an interval $[(1^n), \mu]$ in reverse lexicographic order, is Schur-positive. Here we investigate this conjecture and establish its truth in the following special cases: for $\mu\in [(n-4,1^4), (n)]$  or $\mu\in [(1^n), (3,1^{n-3})], $ or $\mu=(3, 2^k, 1^r)$ when $k\geq 1$ and $0\leq r\leq 2.$  Many new Schur positivity questions are presented.
Extensions of Set Partitions and Permutations
Authors: Caicedo Jhon B. , Moll Victor H. , Ramírez José L. , Villamizar Diego
Published: January 2020

Extensions of a set partition obtained by imposing bounds on the size of the parts is examined. Arithmetical and combinatorial properties of these sequences are established.
Support Equalities Among Ribbon Schur Functions
Authors: Gaetz Marisa , Hardt Will , Sridhar Shruthi
Published: January 2020

In 2007, McNamara proved that two skew shapes can have the same Schur support only if they have the same number of $k \times \ell$ rectangles as subdiagrams. This implies that two ribbons can have the same Schur support only if one is obtained by permuting row lengths of the other. We present substantial progress towards classifying when a permutation $\pi \in S_m$ of row lengths of a ribbon $\alpha$ produces a ribbon $\alpha_{\pi}$ with the same Schur support as $\alpha$; when this occurs for all $\pi \in S_m$, we say that $\alpha$ has full equivalence class. Our main results include a sufficient condition for a ribbon $\alpha$ to have full equivalence class. Additionally, we prove a separate necessary condition, which we conjecture to be sufficient.
Regularity and $h$-Polynomials of Edge Ideals
Authors: Hibi Takayuki , Matsuda Kazunori , Van Tuyl Adam
Published: January 2020

For any two integers $d,r \geqslant 1$, we show that there exists an edge ideal $I(G)$ such that ${\rm reg}\left(R/I(G)\right)$, the Castelnuovo-Mumford regularity of $R/I(G)$, is $r$, and $\deg h_{R/I(G)}(t)$, the degree of the $h$-polynomial of $R/I(G)$, is $d$. Additionally, if $G$ is a graph on $n$ vertices, we show that ${\rm reg}\left(R/I(G)\right) + \deg h_{R/I(G)}(t) \leqslant n$.
The Rank Function of a Positroid and Non-Crossing Partitions
Authors: Mcalmon Robert , Oh Suho
Published: January 2020

A positroid is a special case of a realizable matroid, that arose from the study of totally nonnegative part of the Grassmannian by Postnikov. Postnikov demonstrated that positroids are in bijection with certain interesting classes of combinatorial objects, such as Grassmann necklaces and decorated permutations. The bases of a positroid can be described directly in terms of the Grassmann necklace and decorated permutation. In this paper, we show that the rank of an arbitrary set in a positroid can be computed directly from the associated decorated permutation using non-crossing partitions.
Improved Bounds for the Extremal Number of Subdivisions
Authors: Janzer Oliver
Published: January 2020

Let $H_t$ be the subdivision of $K_t$. Very recently, Conlon and Lee have proved that for any integer $t\geq 3$, there exists a constant $C$ such that $\textrm{ex}(n,H_t)\leq Cn^{3/2-1/6^t}$. In this paper, we prove that there exists a constant $C'$ such that $\textrm{ex}(n,H_t)\leq C'n^{3/2-\frac{1}{4t-6}}$.
Inglenook Shunting Puzzles
Authors: Blackburn Simon R.
Published: January 2020

An inglenook puzzle is a classic shunting (switching) puzzle often found on model railway layouts. A collection of wagons sits in a fan of sidings with a limited length headshunt (lead track). The aim of the puzzle is to rearrange the wagons into a desired order (often a randomly chosen order). This article answers the question: When can you be sure this can always be done? The problem of finding a solution in a minimum number of moves is also addressed.
On the Sweep Map for $\vec{k}$-Dyck Paths
Authors: Xin Guoce , Zhang Yingrui
Published: January 2020

Garsia and Xin gave a linear algorithm for inverting the sweep map for Fuss rational Dyck paths in $D_{m,n}$ where $m=kn\pm 1$. They introduced an intermediate family $\mathcal{T}_n^k$ of certain standard Young tableaux. Then inverting the sweep map is done by a simple walking algorithm on a $T\in \mathcal{T}_n^k$. We find their idea naturally extends for $\mathbf{k}^\pm$-Dyck paths, and also for $\mathbf{k}$-Dyck paths (reducing to $k$-Dyck paths for the equal parameter case). The intermediate object becomes a similar type of tableau in $\mathcal{T}_\mathbf{k}$ of different column lengths. This approach is independent of the Thomas-Williams algorithm for inverting the general modular sweep map.
Degree Constrained Orientations in Countable Graphs
Authors: Bernáth Attila , Bruhn Henning
Published: January 2020

Degree constrained orientations are orientations of an (undirected) graph where the in-degree function satisfies given lower and upper bounds. For finite graphs Frank and Gyárfás (1976) gave a necessary and sufficient condition for the existence of such an orientation. We extend their result to countable graphs.
Monomial Ideals of Weighted Oriented Graphs
Authors: Pitones Yuriko , Reyes Enrique , Toledo Jonathan
Published: January 2020

Let $I=I(D)$ be the edge ideal of a weighted oriented graph $D$ whose underlying graph is $G$. We determine the irredundant irreducible decomposition of $I$. Also, we characterize the associated primes and the unmixed property of $I$. Furthermore, we give a combinatorial characterization for the unmixed property of $I$, when $G$ is bipartite, $G$ is a graph with whiskers or $G$ is a cycle. Finally, we study the Cohen–Macaulay property of $I$.
Quandles of Cyclic Type with Several Fixed Points
Authors: Lages António , Lopes Pedro
Published: January 2020

A quandle of cyclic type of order $n$ with $f$ (greater than 1) fixed points is such that, by definition, each of its permutations splits into $f$ cycles of length 1 and one cycle of length $n-f$. In this article we prove that there is only one such connected quandle, up to isomorphism. This is a quandle of order 6 and 2 fixed points, known in the literature as octahedron quandle.
Universality for Random Surfaces in Unconstrained Genus
Authors: Budzinski Thomas , Curien Nicolas , Petri Bram
Published: January 2020

Starting from an arbitrary sequence of polygons whose total perimeter is $2n$, we can build an (oriented) surface by pairing their sides in a uniform fashion. Chmutov & Pittel have shown that, regardless of the configuration of polygons we started with, the degree sequence of the graph obtained this way is remarkably constant in total variation distance and converges towards a Poisson–Dirichlet partition as $n \to \infty$. We actually show that several other geometric properties of the graph are universal. En route we provide an alternative proof of a weak version of the result of Chmutov & Pittel using probabilistic techniques and related to the circle of ideas around the peeling process of random planar maps. At this occasion we also fill a gap in the existing literature by surveying the properties of a uniform random map with $n$ edges. In particular we show that the diameter of a random map with $n$ edges converges in law towards a random variable taking only values in $\{2,3\}$.
Relating Ordinary and Fully Simple Maps via Monotone Hurwitz Numbers
Authors: Borot Gaëtan , Charbonnier Séverin , Do Norman , Garcia-Failde Elba
Published: January 2020

A direct relation between the enumeration of ordinary maps and that of fully simple maps first appeared in the work of the first and last authors. The relation is via monotone Hurwitz numbers and was originally proved using Weingarten calculus for matrix integrals. The goal of this paper is to present two independent proofs that are purely combinatorial and generalise in various directions, such as to the setting of stuffed maps and hypermaps. The main motivation to understand the relation between ordinary and fully simple maps is the fact that it could shed light on fundamental, yet still not well-understood, problems in free probability and topological recursion.
Orthogonal Systems in Vector Spaces over Finite Fields
Authors: Iosevich Alex , Senger Steven
Published: January 2020

We prove that if a subset of the $d$-dimensional vector space over a finite field is large enough, then it contains many $k$-tuples of mutually orthogonal vectors.
Crystals, Semistandard Tableaux and Cyclic Sieving Phenomenon
Authors: Oh Young-Tak , Park Euiyong
Published: January 2020

In this paper, we study a new cyclic sieving phenomenon on the set $\mathsf{SST}_n(\lambda)$ of semistandard Young tableaux with the cyclic action $\mathsf{c}$ arising from its $U_q(\mathfrak{sl}_n)$-crystal structure. We prove that if $\lambda$ is a Young diagram with $\ell(\lambda) < n$ and $\gcd( n, |\lambda| )=1$, then the triple $\left( \mathsf{SST}_n(\lambda), \mathsf{C}, q^{- \kappa(\lambda)} s_\lambda(1,q, \ldots, q^{n-1}) \right) $ exhibits the cyclic sieving phenomenon, where $\mathsf{C}$ is the cyclic group generated by $\mathsf{c}$. We further investigate a connection between $\mathsf{c}$ and the promotion $\mathsf{pr}$ and show the bicyclic sieving phenomenon given by $\mathsf{c}$ and $\mathsf{pr}^n$ for hook shape.
An Analogue of the Thue-Morse Sequence
Authors: Ferrand Emmanuel
Published: January 2020

We consider the finite binary words $Z(n)$, $n \in {\Bbb N}$, defined by the following self-similar process: $Z(0):=0$, $Z(1):=01$, and $Z(n+1):=Z(n)\cdot\overline{Z(n-1)}$, where the dot $\cdot$ denotes word concatenation, and $\overline{w}$ the word obtained from $w$ by exchanging the zeros and the ones. Denote by $Z(\infty)=01110100 \dots$ the limiting word of this process, and by $z(n)$ the $n$'th bit of this word. This sequence $z$ is an analogue of the Thue-Morse sequence. We show that a theorem of Bacher and Chapman relating the latter to a "Sierpiński matrix" has a natural analogue involving $z$. The semi-infinite self-similar matrix which plays the role of the Sierpiński matrix here is the zeta matrix of the poset of finite subsets of ${\Bbb N}$ without two consecutive elements, ordered by inclusion. We observe that this zeta matrix is nothing but the exponential of the incidence matrix of the Hasse diagram of this poset. We prove that the corresponding Möbius matrix has a simple expression in terms of the zeta matrix and the sequence $z$.
Which Chessboards have a Closed Knight's Tour within the Cube?
Authors: DeMaio Joe
Published: January 2020

A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. When the chessboard is translated into graph theoretic terms the question is transformed into the existence of a Hamiltonian cycle. There are two common tours to consider on the cube. One is to tour the six exterior $n\times n$ boards that form the cube. The other is to tour within the $n$ stacked copies of the $n\times n$ board that form the cube. This paper is concerned with the latter. In this paper necessary and sufficient conditions for the existence of a closed knight's tour for the cube are proven.
Non-Commutative Sylvester's Determinantal Identity
Authors: Konvalinka Matjaž
Published: January 2020

Sylvester's identity is a classical determinantal identity with a simple linear algebra proof. We present combinatorial proofs of several non-commutative extensions, and find a $\beta$-extension that is both a generalization of Sylvester's identity and the $\beta$-extension of the quantum MacMahon master theorem.
Pengaruh Kompetensi, Kompensasi, Iklim Organisasi Dan Etos Kerja Pustakawan Terhadap Kinerja Pustakawan Perpustakaan Perguruan Tinggi Di Kota Bandar Lampung
Authors: Fitriani Rd Erni , Utoyo Bambang , Effendi Nur
Published: January 2020

Pada umumnya pustakawan perguruan tinggi negeri di Kota Bandar Lampung mengusulkan kenaikan jabatan fungsional pustakawan lebih dari dua tahun. Ini menunjukkan bahwa kinerja pustakawan tersebut masih rendah. Rendahnya kinerja pustakawan diduga disebabkan oleh beberapa faktor yang mempengaruhinya. Tujuan penelitian ini adalah : 1) menganalisis dan mengkaji pengaruh kompetensi Pustakawan terhadap Kinerja Pustakawan; 2) menganalisis dan mengkaji pengaruh kompensasi Pustakawan terhadap Kinerja Pustakawan; 3) menganalisis dan mengkaji pengaruh iklim organisasi terhadap Kinerja Pustakawan; 4) menganalisis dan mengkaji pengaruh etos kerja Pustakawan terhadap Kinerja Pustakawan; 5) menganalisis dan mengkaji pengaruh kompetensi, kompensasi, iklim organisasi dan etos kerja Pustakawan terhadap Kinerja Pustakawan; Merupakan penelitian deskriptif dan verifikatif yaitu menggambarkan variabelvariabel yang menjadi objek penelitian, yaitu kompetensi, kompensasi, iklim organisasi, etos kerja dan kinerja pustakawan serta menguji kebenaran suatu hipotesis melalui pengumpulan data di lapangan.Metode yang digunakan dalam penelitian adalah kuantitatif dengan teknik total sampling. Pengumpulan data melalui data primer dan data sekunder, menggunakan skala Likert. Teknik pengujian instumen melalui uji validitas dan uji reliabiltas. Analisis data menggunakan analisis deskriptif dan analisis inferensial dengan pengolahan data menggunakan SPSS. Uji hipotesis dengan regresi linear berganda, Uji asumsi klasik meliputi uji t-parsial dan uji fsimultan, uji koefisien determinasi (R2 ), uji normalitas, uji heterokedatisitas dan uji multikorelasi. Hasil dari penelitian ini adalah secara parsial kompetensi berpengaruh sebesar 65,4%,terhadap kinerja pustakwa, kompensasi berpengaruh sebesr 62,6% terhadap kinerja pustakawan, iklim organisai berpengaruh sebesar 59,4% terhadap kinerja pustakawan, dan etos kerja berpengaruh sebesar 53% terhadap kinerja pustakawan dan secara simultan kompetensi, kompensasi, iklim organisasi dan etos kerja berpengaruh sebesar 88,9% terhadap kinerja pustakawan Perpustakaan Perguruan Tinggi Negeri di Kota Bandar Lampung
Kualitas Pelayanan Sub Bagian Umum Dan Kepegawaian Rumah Sakit Umum Daerah (RSUD) Sukadana Kabupaten Lampung Timur
Authors: Asyadi Dodi , Widodo Tri , Setioko Sigit
Published: January 2020

Pelayanan publik ini menjadi semakin penting karena senantiasa berhubungan dengan khalayak masyarakat ramai yang memiliki keanekaragaman kepentingan dan tujuan. Penelitian ini ditulis dengan pendekatan kualitatif deskriptif. Data diperoleh melalui wawancara mendalam, data dokumentasi dan observasi. Hasil penelitian, maka dapat disimpulkan bahwa pelayanan Sub Bagian Umum dan Pepegawaian di RSUD Sukadana yakni: (1) Terkadang terdapat pegawai yang lain kurang puas akan kinerja yang telah diberikan. (2) Dapat menjalin rasa keadilan artinya terdapat keterbukaan dalam memberikan pelayanan tidak membeda-bedakan dan memberkan perlakuan terhadap individu atau sekelompok orang dalam keadaan yang sama. (3) Dapat mengerjakan dengan waktu yang cepat, tepat waktu, menyenangkan dan dapat diandalkan. (4) Pelayanan yang efisien ekonomis dan efisien, dapat dijangkau dengan tarifdan pajak yang dapat diterima pada semua lapisan pegawai di RSUD Sukadana Kabupaten Lampung Timur.
KEGAGALAN PRIVATISASI BUMN DI ERA REZIM ORDE BARU DALAM PERSPEKTIF EKONOMI POLITIK
Authors: Ma'arif Syamsul
Published: January 2020

After had being carried out nationalization and hostility against west countries, the New Order regime made important decision to change Indonesia economic direction from etatism system to free market economy. A set of policies were taken in order private sector could play major role in economic. However, when another economic sectors were reformed substantially, effords to reform the State Owned Enterprises had failed. The State Owned Enterprise, in fact, remained to play dominant role like early years of guided democracy era. Role of the State Owned Enterprises was more and more powerfull). The main problem of reforms finally lied on reality that vested interest of bureaucrats (civil or military) was so large that could’nt been overcome.
PERAN BAWASLU DALAM MENCEGAH MONEY POLITICS DALAM PEMLIHAN GUBERNUR PROVINSI LAMPUNG TAHUN 2018
Authors: Shela Metria , Sutiyo Sutiyo
Published: January 2020

Demokrasi dan pelaksaanaan pemilu bagaikan dua sisi mata uang yang tidak dapat dipisahkan. Pelaksaaan pemilu merupakan salah satu indikator berjalanya demokrasi di negara demokratis. Sebagai negara demokratis Indonesia melaksanakan pemilihan kepala daerah setingkat gubernur setiap lima tahun sekali. Di Provinsi Lampung telah diselenggarakan pemilihan gubernur pada tahun 2018. Namun, penyelenggaraan pemilu tersebut diwarnai dengan adanya money politic atau adanya politik uang. Money politics merupakan salah satu pelanggaran dalam pelaksanaan pemilihan umum. Tulisan ini bertujuan untuk melihat efektivitas peran bawaslu dalam mencegah money politics pada pilkada di Provinsi Lampung tahun 2018. Penelitian ini menggunakan merupakan penelitian kualitatif deskriptif, dan menggunakan jenis data sekunder yang didapatkan dari informan serta menggunakan teknik analisis data yang disarankan oleh Miles dan Hubberman (2002) yang terdiri dari reduksi data, display data dan penarikan kesimpulan. Penelitian ini menghasilkan kesimpulan bahwa Bawaslu kecamatan Terbanggi Besar telah melaksanakan tugas dengan baik namun tetep tidak maksimal karena adanya keterbatasan wewenang
Bulbophyllum papuaense (Orchidaceae), a new species from Indonesia
Authors: Lin Dongliang , Zhou Kailing , Hidayat Arief , Jin Xiao-Hua
Published: January 2020

A new species, Bulbophyllum papuaense, was described and illustrated from Indonesia. Bulbophyllum papuaense is similar to Bulbophyllum tortuosum and B. muscohaerens but differs from them by having rhizome and pseudobulbs covered with papillose scales, caudate and ciliate petals, linear and ciliate lip.
Des revendications ordinaires aux mobilisations citoyennes : la conquête du droit à la ville dans des quartiers informels de Batna (Algérie)
Authors: Belmessous Fatiha , Naceur Farida
Published: January 2020

Cet article vise à comprendre comment au sein du système semi-autoritaire algérien émergent diverses formes de mobilisation, qu’elles traduisent une volonté d’accéder aux nécessaires ressources urbaines ou de participer à la vie politique locale. Pour l’illustrer, nous avons choisi de présenter la construction de légitimités citoyennes à la suite de différents récits, individuels et collectifs, dans une ville moyenne de l’Est algérien (la ville de Batna) au sein de quartiers non réglementaires. Le choix des quartiers informels (c’est-à-dire conçus en dehors de la planification et de la réglementation) comme cadre d’analyse de ces mobilisations citoyennes s’explique par la dynamique et la capacité de revendication de leurs résidents pour l’amélioration de leur vie quotidienne. Ce qui nous intéresse particulièrement est d’analyser le passage de revendications localisées à la construction de véritables légitimités, et par-là, à la reconnaissance de ces habitants comme des citoyens ordinaires au sein de la ville (en dépit du caractère informel de leurs lieux de vie). Comment les populations de ces quartiers parviennent-elles à développer une capacité d’organisation et de mobilisation pour construire leur propre légitimité ? Comment interagissent-elles avec les sphères du pouvoir alors qu’elles vivent en dehors de la légalité juridique ?
Citadinités et droits à la ville au Sud : les minorités à l’épreuve de l’invisible (Maputo, Rio de Janeiro, Mexico)
Authors: Faret Laurent , Fournet-Guérin Catherine , Ginisty Karine , Michel Aurélia , Perraudin Anna
Published: January 2020

Cet article se propose d’analyser les formes d’invisibilité de groupes stigmatisés (migrants, minorités racialisées, prostituées) dans différentes capitales de pays dits du Sud. Dans des contextes de domination (autoritarisme politique, marginalisation sociale et spatiale) dans lesquels contester les injustices subies serait trop coûteux, voire dangereux, l’invisibilité peut constituer une stratégie inscrite dans la vie quotidienne, qui permet de consolider sa présence et de se projeter en ville en épousant les figures citadines légitimes. Il n’y a alors pas de mobilisation collective autour de la reconnaissance des groupes ou du renversement des figures du stigmate, mais plutôt des stratégies d’anonymisation et de banalisation, qui se donnent à voir dans des pratiques de l’espace urbain, des habitudes et des expériences ordinaires. Il s’agit alors de s’interroger sur les formes et les conditions de cette invisibilité. On montrera que ces groupes peuvent accéder à des formes de tranquillité dans la manière d’être citadins, et ce en dépit même de leur vulnérabilité. C’est même leur seule possibilité pour affirmer leur place en ville et ainsi acquérir une forme de légitimité aux yeux des autres citadins. Loin d’être envisagé de manière normative ou revendicative, le droit à la ville prend alors la forme d’un droit à la discrétion, à être là, à vivre en ville comme n’importe quel autre. Les auteurs confrontent des expériences de terrain issues de trois villes (Maputo, Rio de Janeiro, Mexico), mettant ainsi en relation des contextes latino-américains et africains souvent séparés dans la littérature scientifique.
Simone de Beauvoir — La Pléiade
Authors: Le Bon de Beauvoir Sylvie , Jeannelle Jean-Louis , Adler Laure
Published: January 2020

L’entretien est centré sur la sortie en mai 2018 des Mémoires de Simone de Beauvoir, deux tomes accompagnés d’un album biographique illustré, dans la Bibliothèque de la Pléiade (éditions Gallimard). Il évoque la personne, l’œuvre littéraire et la pensée de Simone de Beauvoir à la fois à partir du témoignage vécu de sa fille adoptive Sylvie Le Bon de Beauvoir et de l’approche universitaire de Jean-Louis Jeannelle.
Le Deuxième sexe
Authors: Le Bon de Beauvoir Sylvie
Published: January 2020

On constate, 26 ans après la parution du Deuxième sexe , l’extension mondiale du féminisme. Cependant la pensée de l’œuvre, que résume la formule explosive « On ne naît pas femme, on le devient », est souvent déformée. L’article en rappelle le sens : aucune essence, aucune nature, aucun destin ne définit l’être des femmes, mais pour qu’elles accèdent à la libre existence, une lutte, tant individuelle que collective, est nécessaire.
Une nouvelle traduction du Deuxième sexe
Authors: Borde Constance , Malovany-Chevallier Sheila
Published: January 2020

La nouvelle et tant attendue traduction anglaise du Deuxième sexe fut publiée en 2009. La traduction de la phrase « One is not born, but rather becomes, woman » (dont on supprime l’article indéfini « a » devant « woman ») apporte un nouveau regard sur le sens du texte. Chaque mot résulte d’un choix qui restituera fidèlement la voix et les idées de Beauvoir.
La question de la discipline dans le développement de l’Armée de terre japonaise à l’époque de Meiji (1868-1912)
Authors: Seizelet Éric
Published: January 2020

Cet article vise à identifier la place de la discipline militaire lors de la phase de création, puis de développement d’un appareil militaire moderne dans le Japon de Meiji. Il s’appuie sur les différents instruments, politiques, administratifs, juridiques, psychologiques mis en place à cet effet par le haut commandement afin de sécuriser la « neutralité » politique des nouvelles forces armées dans cette phase délicate de transition. Il mesure l’impact des guerres contre la Chine et la Russie, au moment même où la question de la discipline militaire devient un enjeu majeur, non seulement pour légitimer le service militaire à l’intérieur, mais aussi pour consolider la position internationale du Japon en tant que nation « civilisée ».
Entre apolitisme et anticommunisme. Les officiers des états-majors généraux et le Front populaire, 1936-1937
Authors: Catros Simon
Published: January 2020

L’histoire politique et sociale des officiers français à l’époque républicaine a mis en évidence un rapport particulier de ceux-ci au politique. En leur sein, les officiers des états-majors généraux représentent un groupe socioprofessionnel spécifique, exerçant leur activité au service ou à proximité immédiate de décideurs gouvernementaux. Dans les années trente, la plupart d’entre eux, d’opinions globalement conservatrices, étaient familiers du monde politique et parlementaire. La victoire électorale du Front populaire généra cependant durant le second semestre 1936 une véritable « psychose » alimentée par les rumeurs de putsch communiste lancées par les milieux d’extrême droite. L’apaisement survint dès les premières semaines de l’année 1937. Finalement, l’historien doit constater que les officiers des états-majors généraux demeurèrent légalistes en dépit de tentations.
Giant Facial Hemangioma of Infancy
Authors: Arevalo-Coutinho Fernando , Arevalo J. Fernando
Published: January 2020

A monthly case study, featured in Journal of Pediatric Ophthalmology & Strabismus, showing encounters in the field of Pediatric Ophthalmology.
Accounting Information Systems (AIS) in SMEs
Authors: Ibrahim Fahmi , Ali Diyana Najwa Haji , Besar Nur Suaidah Awang
Published: January 2020

Small-medium enterprises (SMEs) have always been considered to be the backbone of Brunei's economy. As published by the OECD in 2006, SMEs constitute a high percentage of businesses, where they account for 98% of all active business enterprises, and contribute about 92% of the employment in the private sector, and at least 66% of the GDP within the non-oil sector of the economy. Since SMEs are considered to be significant for the economy, they are encouraged to improve their business performance in order to sustain their business development by enhancing their accounting information system. This article will focus on the current accounting practices in which Brunei SMEs have been implemented by MMA Cube Stores as a case study. As cube shop businesses have been growing all over the country, it is significant to carry out this research as it may apply to the other similar business in Brunei. Reasonable recommendations are included in this article for the augmentation of the accounting system among Brunei SMEs.
Deep-Analysis of Palmprint Representation Based on Correlation Concept for Human Biometrics Identification
Authors: Mokni Raouia , Drira Hassen , Kherallah Monji
Published: January 2020

The security of people requires a beefy guarantee in our society, particularly, with the spread of terrorism throughout the world. In this context, palmprint identification based on texture analysis is amongst the pattern recognition applications to recognize people. In this article, the researchers investigated a deep texture analysis for the palmprint texture pattern representation based on a fusion between several texture information extractions through multiple descriptors, such as HOG and Gabor Filters, Fractal dimensions and GLCM corresponding respectively to the frequency, model, and statistical methodologies-based texture features. They assessed the proposed deep texture analysis method as well as the applicability of the dimensionality reduction techniques and the correlation concept between the features-based fusion on the challenging PolyU, CASIA and IIT-Delhi Palmprint databases. The experimental results show that the fusion of different texture types using the correlation concept for palmprint modality identification leads to promising results.