bluuebunny/crossref_metadata_2025_split huggingface dataset:
Flag enumerations of matroid base polytopes
Authors: Kim Sangwook 
Published: August 2021

In this paper, we study flag structures of matroid base polytopes. We describe faces of matroid base polytopes in terms of matroid data, and give conditions for hyperplane splits of matroid base polytopes. Also, we show how the $\textbf{cd}$-index of a polytope can be expressed when a polytope is cut by a hyperplane, and apply these to the $\textbf{cd}$-index of a matroid base polytope of a rank $2$ matroid.
Dans cet article, nous étudions les structures de drapeau de polytopes de base de matroïde. Nous décrivons des faces de polytopes de base de matroïde en terme des données de matroïde, et donnons des conditions pour les divisions de hyperplane de polytopes de base de matroïde. Nous montrons également comment le $\mathbf{cd}$-index d’un polytope peut être exprimé quand un polytope est coupé par un hyperplane, et appliquons ceux-ci au $\mathbf{cd}$-index d’un polytope de base de matroïde d’un rang $2$ matroïde.
Distances in random Apollonian network structures
Authors: Bodini Olivier , Darrasse Alexis , Soria Michèle 
Published: August 2021

In this paper, we study the distribution of distances in random Apollonian network structures (RANS), a family of graphs which has a one-to-one correspondence with planar ternary trees. Using multivariate generating functions that express all information on distances, and singularity analysis for evaluating the coefficients of these functions, we prove a Rayleigh limit distribution for distances to an outermost vertex, and show that the average value of the distance between any pair of vertices in a RANS of order $n$ is asymptotically $\sqrt{n}$.
Nous étudions dans ce papier la distribution des distances dans les structures des réseaux apolloniens aléatoires (RANS), une famille de graphes en bijection avec les arbres ternaires planaires. En s'appuyant sur l'utilisation de séries génératrices multivariées pour décrire toute l'information sur les distances, ainsi que sur l'analyse de singularités pour évaluer les coefficients de ces séries, nous prouvons une distribution limite de Rayleigh pour les distances vers un sommet externe du RANS et montrons que la distance moyenne entre deux sommets quelconques d'un RANS d'ordre $n$ est asymptotiquement $\sqrt{n}$.
From Bruhat intervals to intersection lattices and a conjecture of Postnikov
Authors: Hultman Axel , Linusson Svante , Shareshian John , Sjöstrand Jonas 
Published: August 2021

We prove the conjecture of A. Postnikov that ($\mathrm{A}$) the number of regions in the inversion hyperplane arrangement associated with a permutation $w \in \mathfrak{S}_n$ is at most the number of elements below $w$ in the Bruhat order, and ($\mathrm{B}$) that equality holds if and only if $w$ avoids the patterns $4231$, $35142$, $42513$ and $351624$. Furthermore, assertion ($\mathrm{A}$) is extended to all finite reflection groups.
Nous prouvons la conjecture de A. Postnikov que ($\mathrm{A}$) le nombre de régions dans l'arrangement d'hyperplans inverses associés à la permutation $w \in \mathfrak{S}_n$ est au plus égal au nombre d'éléments en dessous de $w$ dans l'ordre de Bruhat, et ($\mathrm{B}$) il y a égalité si et seulement si $w$ évite les motifs $4231$, $35142$, $42513$ et $351624$. De plus, l'affirmation ($\mathrm{A}$) est généralisée à tous les groupes de réflexion finis.
$(\ell, 0)$-Carter Partitions and their crystal theoretic interpretation
Authors: Berg Chris , Vazirani Monica 
Published: August 2021

In this paper we give an alternate combinatorial description of the "$(\ell,0)$-Carter partitions''. Our main theorem is the equivalence of our combinatoric and the one introduced by James and Mathas ($\textit{A q-analogue of the Jantzen-Schaper theorem}$). The condition of being an $(\ell,0)$-Carter partition is fundamentally related to the hook lengths of the partition. The representation-theoretic significance of their combinatoric on an $\ell$-regular partition is that it indicates the irreducibility of the corresponding Specht module over the finite Hecke algebra. We use our result to find a generating series which counts the number of such partitions, with respect to the statistic of a partition's first part. We then apply our description of these partitions to the crystal graph $B(\Lambda_0)$ of the basic representation of $\widehat{\mathfrak{sl}_{\ell}}$, whose nodes are labeled by $\ell$-regular partitions. Here we give a fairly simple crystal-theoretic rule which generates all $(\ell,0)$-Carter partitions in the graph of $B(\Lambda_0)$.
Dans cet article, nous donnons une description combinatoire alternative des partitions "$(\ell,0)$-Carter". Notre théorème principal est une équivalence entre notre combinatoire et celle introduite par James et Mathas ($\textit{A q-analogue of the Jantzen-Schaper theorem}$). La propriété $(\ell,0)$-Carter est fondamentalement liée aux longueurs des équerres de la partition. En terme de théorie des représentations, leur combinatoire pour une partition $\ell$-régulière permet de déterminer l'irréducibilité du module de Specht spécialisé sur l’algèbre de Hecke finie. Nous utilisons notre résultat pour déterminer leur série génératrice en fonction de la taille de la première part. Nous utilisons ensuite notre description de ces partitions au graphe cristallin $B(\Lambda _0)$ de la représentation basique de $\widehat{\mathfrak{sl}_{\ell}}$, dont les nœuds sont étiquetés par les partitions $\ell$-régulières. Nous donnons une règle cristalline relativement simple permettant d'engendrer toutes les partitions $\ell$-régulières $(\ell,0)$-Carter dans le graphe de $B(\Lambda _0)$.
Independent sets in graphs with an excluded clique minor
Authors: Wood David R. 
Published: August 2021

Graphs and Algorithms
Let G be a graph with n vertices, with independence number α, and with no Kt+1-minor for some t ≥ 5. It is proved that (2α - 1)(2t - 5) ≥ 2n - 5. This improves upon the previous best bound whenever n≥2/5t2.
On the tileability of polygons with colored dominoes
Authors: Worman Chris , Yang Boting 
Published: August 2021

Analysis of Algorithms
We consider questions concerning the tileability of orthogonal polygons with colored dominoes. A colored domino is a rotatable 2 × 1 rectangle that is partitioned into two unit squares, which are called faces, each of which is assigned a color. In a colored domino tiling of an orthogonal polygon P, a set of dominoes completely covers P such that no dominoes overlap and so that adjacent faces have the same color. We demonstrated that for simple layout polygons that can be tiled with colored dominoes, two colors are always sufficient. We also show that for tileable non-simple layout polygons, four colors are always sufficient and sometimes necessary. We describe an O(n) time algorithm for computing a colored domino tiling of a simple orthogonal polygon, if such a tiling exists, where n is the number of dominoes used in the tiling. We also show that deciding whether or not a non-simple orthogonal polygon can be tiled with colored dominoes is NP-complete.
Arithmetics in β-numeration
Authors: Bernat Julien 
Published: August 2021

Analysis of Algorithms
The β-numeration, born with the works of Rényi and Parry, provides a generalization of the notions of integers, decimal numbers and rational numbers by expanding real numbers in base β, where β>1 is not an integer. One of the main differences with the case of numeration in integral base is that the sets which play the role of integers, decimal numbers and rational numbers in base β are not stable under addition or multiplication. In particular, a fractional part may appear when one adds or multiplies two integers in base β. When β is a Pisot number, which corresponds to the most studied case, the lengths of the finite fractional parts that may appear when one adds or multiplies two integers in base β are bounded by constants which only depend on β. We prove that, for any Perron number β, the set of finite or ultimately periodic fractional parts of the sum, or the product, of two integers in base β is finite. Additionally, we prove that it is possible to compute this set for the case of addition when β is a Parry number. As a consequence, we deduce that, when β is a Perron number, there exist bounds, which only depend on β, for the lengths of the finite fractional parts that may appear when one adds or multiplies two integers in base β. Moreover, when β is a Parry number, the bound associated with the case of addition can be explicitly computed.
A lower bound for approximating the Grundy number
Authors: Kortsarz Guy 
Published: August 2021

Graphs and Algorithms
The grundy numbering of a graph is the maximum number of colors used by on-line first-fit coloring, under the worst order of arrival of vertices. The grundy numbering problem is to find this ordering. We prove that there is a constant c>1 so that approximating the grundy numbering problem within c is not possible, unless NP ⊆ RP
Tribes of cubic partial cubes
Authors: Klavžar Sandi , Shpectorov Sergey 
Published: August 2021

Graphs and Algorithms
Partial cubes are graphs isometrically embeddable into hypercubes. Three infinite families and a few sporadic examples of cubic partial cubes are known. The concept of a tribe is introduced as means to systematize the known examples and establish relations among them. Efficient methods of computation of tribes are developed and several concrete tribes, that include known, as well as new cubic partial cubes, are computed by hand and with the use of a computer.
Asymptotic behaviour of a non-commutative rational series with a nonnegative linear representation
Authors: Dumas Philippe , Lipmaa Helger , Wallén Johan 
Published: August 2021

Analysis of Algorithms
We analyse the asymptotic behaviour in the mean of a non-commutative rational series, which originates from differential cryptanalysis, using tools from probability theory, and from analytic number theory. We derive a Fourier representation of a first-order summation function obtained by interpreting this rational series as a non-classical rational sequence via the octal numeration system. The method is applicable to a wide class of sequences rational with respect to a numeration system essentially under the condition that they admit a linear representation with nonnegative coefficients.
"Trivializing'' generalizations of some Izergin-Korepin-type determinants
Authors: Amdeberhan Tewodros , Zeilberger Doron 
Published: August 2021

Combinatorics
We generalize (and hence trivialize and routinize) numerous explicit evaluations of determinants and pfaffians due to Kuperberg, as well as a determinant of Tsuchiya. The level of generality of our statements render their proofs easy and routine, by using Dodgson Condensation and/or Krattenthaler's factor exhaustion method.
FP/FIFO scheduling: coexistence of deterministic and probabilistic QoS guarantees
Authors: Minet Pascale , Martin Steven , Saidane Leila Azouz , Azzaz Skander 
Published: August 2021

Distributed Computing and Networking
In this paper, we focus on applications having quantitative QoS (Quality of Service) requirements on their end-to-end response time (or jitter). We propose a solution allowing the coexistence of two types of quantitative QoS garantees, deterministic and probabilistic, while providing a high resource utilization. Our solution combines the advantages of the deterministic approach and the probabilistic one. The deterministic approach is based on a worst case analysis. The probabilistic approach uses a mathematical model to obtain the probability that the response time exceeds a given value. We assume that flows are scheduled according to non-preemptive FP/FIFO. The packet with the highest fixed priority is scheduled first. If two packets share the same priority, the packet arrived first is scheduled first. We make no particular assumption concerning the flow priority and the nature of the QoS guarantee requested by the flow. An admission control derived from these results is then proposed, allowing each flow to receive a quantitative QoS guarantee adapted to its QoS requirements. An example illustrates the merits of the coexistence of deterministic and probabilistic QoS guarantees.
Exponential bounds and tails for additive random recursive sequences
Authors: Rüschendorf Ludger , Schopp Eva-Maria 
Published: August 2021

Analysis of Algorithms
Exponential bounds and tail estimates are derived for additive random recursive sequences, which typically arise as functionals of recursive structures, of random trees or in recursive algorithms. In particular they arise as parameters of divide and conquer type algorithms. We derive tail bounds from estimates of the Laplace transforms and of the moment sequences. For the proof we use some classical exponential bounds and some variants of the induction method. The paper generalizes results of Rösler (% \citeyearNPRoesler:91, % \citeyearNPRoesler:92) and % \citeNNeininger:05 on subgaussian tails to more general classes of additive random recursive sequences. It also gives sufficient conditions for tail bounds of the form \exp(-a t^p) which are based on a characterization of \citeNKasahara:78.
Strong chromatic index of products of graphs
Authors: Togni Olivier 
Published: August 2021

Graphs and Algorithms
The strong chromatic index of a graph is the minimum number of colours needed to colour the edges in such a way that each colour class is an induced matching. In this paper, we present bounds for strong chromatic index of three different products of graphs in term of the strong chromatic index of each factor. For the cartesian product of paths, cycles or complete graphs, we derive sharper results. In particular, strong chromatic indices of d-dimensional grids and of some toroidal grids are given along with approximate results on the strong chromatic index of generalized hypercubes.
Shifts with decidable language and non-computable entropy
Authors: Hertling Peter , Spandl Christoph 
Published: August 2021

Automata, Logic and Semantics
We consider subshifts of the full shift of all binary bi-infinite sequences. On the one hand, the topological entropy of any subshift with computably co-enumerable language is a right-computable real number between 0 and 1. We show that, on the other hand, any right-computable real number between 0 and 1, whether computable or not, is the entropy of some subshift with even polynomial time decidable language. In addition, we show that computability of the entropy of a subshift does not imply any kind of computability of the language of the subshift
Progress on the traceability conjecture for oriented graphs
Authors: Frick Marietjie , Katrenič Peter 
Published: August 2021

Graphs and Algorithms
A digraph is k-traceable if each of its induced subdigraphs of order k is traceable. The Traceability Conjecture is that for k ≥ 2 every k-traceable oriented graph of order at least 2k − 1 is traceable. The conjecture has been proved for k ≤ 5. We prove that it also holds for k = 6.
A note on compact and compact circular edge-colorings of graphs
Authors: Dereniowski Dariusz , Nadolski Adam 
Published: August 2021

Graphs and Algorithms
We study two variants of edge-coloring of edge-weighted graphs, namely compact edge-coloring and circular compact edge-coloring. First, we discuss relations between these two coloring models. We prove that every outerplanar bipartite graph admits a compact edge-coloring and that the decision problem of the existence of compact circular edge-coloring is NP-complete in general. Then we provide a polynomial time 1:5-approximation algorithm and pseudo-polynomial exact algorithm for compact circular coloring of odd cycles and prove that it is NP-hard to optimally color these graphs. Finally, we prove that if a path P2 is joined by an edge to an odd cycle then the problem of the existence of a compact circular coloring becomes NP-complete.
Counting descents, rises, and levels, with prescribed first element, in words
Authors: Kitaev Sergey , Mansour Toufik , Remmel Jeff 
Published: August 2021

Combinatorics
Recently, Kitaev and Remmel refined the well-known permutation statistic "descent" by fixing parity of one of the descent's numbers which was extended and generalized in several ways in the literature. In this paper, we shall fix a set partition of the natural numbers N,(N1, ..., Ns), and we study the distribution of descents, levels, and rises according to whether the first letter of the descent, rise, or level lies in Ni over the set of words over the alphabet [k] = 1, ..., k. In particular, we refine and generalize some of the results by Burstein and Mansour
Waiting Time Distribution for Pattern Occurrence in a Constrained Sequence: an Embedding Markov Chain Approach
Authors: Nuel Gregory 
Published: August 2021

Analysis of Algorithms
In this paper we consider the distribution of a pattern of interest in a binary random (d; k)-sequence generated by a Markov source. Such constrained sequences are frequently encountered in communication systems. Unlike the previous approach based on generating function we have chosen here to use Markov chain embedding techniques. By doing so, we get both previous results (sequence constrained up to the rth occurrence), and new ones (sequence constrained up to its end). We also provide in both cases efficient algorithms using basic linear algebra only. We then compare our numerical results to previous ones and finally propose several interesting extensions of our method which further illustrate the usefulness of our approach. That is to say higher order Markov chains, renewal occurrences rather than overlapping ones, heterogeneous models, more complex patterns of interest, and multistate trial sequences.
Diophantine Approximation, Ostrowski Numeration and the Double-Base Number System
Authors: Berthe Valerie , Imbert Laurent 
Published: August 2021

Analysis of Algorithms
A partition of $x > 0$ of the form $x = \sum_i 2^{a_i}3^{b_i}$ with distinct parts is called a double-base expansion of $x$. Such a representation can be obtained using a greedy approach, assuming one can efficiently compute the largest \mbox{$\{2,3\}$-integer}, i.e., a number of the form $2^a3^b$, less than or equal to $x$. In order to solve this problem, we propose an algorithm based on continued fractions in the vein of the Ostrowski number system, we prove its correctness and we analyse its complexity. In a second part, we present some experimental results on the length of double-base expansions when only a few iterations of our algorithm are performed.
Edge condition for long cycles in bipartite graphs
Authors: Adamus Lech 
Published: August 2021

Graphs and Algorithms
The following problem was solved by Woodall in 1972: for any pair of nonnegative integers n and k < n/2 - 1 find the minimum integer g(n, k) such that every graph with n vertices and at least g(n, k) edges contains a cycle of length n - k. Woodall proved even more: the size g(n, k), in fact, guarantees the existence of cycles C, for all 3 <= p <= n - k. <br> <br> In the paper an analogous problem for bipartite graphs is considered. It is proved that every bipartite graph with color classes of cardinalities m and n, m <= n, and size greater than n(m - k - 1) + k + 1 contains a cycle of length 2m - 2k, where m >= 1/2k(2) + 3/2k + 4, k is an element of N. The bound on the number of edges is best possible. Moreover, this size condition guarantees the existence of cycles of all even lengths up to 2m - 2k. We also characterize all extremal graphs for this problem. Finally, we conjecture that the condition on the order may be relaxed to m >= 2k + 2.
On the chromatic number of some flip graphs
Authors: Fabila-Monroy Ruy , Flores-Peñaloza David , Huemer Clemens , Hurtado Ferran , Urrutia Jorge , Wood David R. 
Published: August 2021

Graphs and Algorithms
This paper studies the chromatic number of the following four flip graphs (under suitable definitions of a flip): the flip graph of perfect matchings of a complete graph of even order, the flip graph of triangulations of a convex polygon (the associahedron), the flip graph of non-crossing Hamiltonian paths of a set of points in convex position, and the flip graph of triangles in a convex point set. We give tight bounds for the latter two cases and upper bounds for the first two.
String pattern avoidance in generalized non-crossing trees
Authors: Sun Yidong , Wang Zhiping 
Published: August 2021

Combinatorics
The problem of string pattern avoidance in generalized non-crossing trees is studied. The generating functions for generalized non-crossing trees avoiding string patterns of length one and two are obtained. The Lagrange inversion formula is used to obtain the explicit formulas for some special cases. A bijection is also established between generalized non-crossing trees with special string pattern avoidance and little Schr ̈oder paths.
Long cycles in hypercubes with distant faulty vertices
Authors: Gregor Petr , Škrekovski Riste 
Published: August 2021

Graphs and Algorithms
In this paper, we study long cycles in induced subgraphs of hypercubes obtained by removing a given set of faulty vertices such that every two faults are distant. First, we show that every induced subgraph of Q(n) with minimum degree n - 1 contains a cycle of length at least 2(n) - 2(f) where f is the number of removed vertices. This length is the best possible when all removed vertices are from the same bipartite class of Q(n). Next, we prove that every induced subgraph of Q(n) obtained by removing vertices of some given set M of edges of Q(n) contains a Hamiltonian cycle if every two edges of M are at distance at least 3. The last result shows that the shell of every linear code with odd minimum distance at least 3 contains a Hamiltonian cycle. In all these results we obtain significantly more tolerable faulty vertices than in the previously known results. We also conjecture that every induced subgraph of Q(n) obtained by removing a balanced set of vertices with minimum distance at least 3 contains a Hamiltonian cycle.
Enumeration of words by the sum of differences between adjacent letters
Authors: Mansour Toufik 
Published: August 2021

Combinatorics
We consider the sum u of differences between adjacent letters of a word of n letters, chosen uniformly at random from a given alphabet. This paper obtains the enumerating generating function for the number of such words with respect to the sum u, as well as explicit formulas for the mean and variance of u.
The Eulerian distribution on centrosymmetric involutions
Authors: Barnabei Marilena , Bonetti Flavio , Silimbani Matteo 
Published: August 2021

Combinatorics
We present an extensive study of the Eulerian distribution on the set of centrosymmetric involutions, namely, involutions in S(n) satisfying the property sigma(i) + sigma(n + 1 - i) = n + 1 for every i = 1 ... n. We find some combinatorial properties for the generating polynomial of such distribution, together with an explicit formula for its coefficients. Afterwards, we carry out an analogous study for the subset of centrosymmetric involutions without fixed points.
Binary Labelings for Plane Quadrangulations and their Relatives
Authors: Felsner Stefan , Huemer Clemens , Kappes Sarah , Orden David 
Published: August 2021

Graphs and Algorithms
Motivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two trees). Our labeling resembles many of the properties of Schnyder's one for triangulations: Apart from being in bijection with tree decompositions, paths in these trees allow to define the regions of a vertex such that counting faces in them yields an algorithm for embedding the quadrangulation, in this case on a 2-book. Furthermore, as Schnyder labelings have been extended to 3-connected plane graphs, we are able to extend our labeling from quadrangulations to a larger class of 2-connected bipartite graphs.