bluuebunny/crossref_metadata_2025_split huggingface dataset:
The $r$-Matching Sequencibility of Complete Graphs
Authors: Mammoliti Adam 
Published: January 2020

Alspach [ Bull. Inst. Combin. Appl., 52 (2008), pp. 7--20] defined the maximal matching sequencibility of a graph $G$, denoted $ms(G)$, to be the largest integer $s$ for which there is an ordering of the edges of $G$ such that every $s$ consecutive edges form a matching. Alspach also proved that $ms(K_n) = \bigl\lfloor\frac{n-1}{2}\bigr\rfloor$. Brualdi et al. [Australas. J. Combin., 53 (2012), pp. 245--256] extended the definition to cyclic matching sequencibility of a graph $G$, denoted $cms(G)$, which allows cyclical orderings and proved that $cms(K_n) = \bigl\lfloor\frac{n-2}{2}\bigr\rfloor$.In this paper, we generalise these definitions to require that every $s$ consecutive edges form a subgraph where every vertex has degree at most $r\geq 1$, and we denote the maximum such number for a graph $G$ by $ms_r(G)$ and $cms_r(G)$ for the non-cyclic and cyclic cases, respectively. We conjecture that $ms_r(K_n) = \bigl\lfloor\frac{rn-1}{2}\bigr\rfloor$ and ${\bigl\lfloor\frac{rn-1}{2}\bigr\rfloor-1}\leq cms_r(K_n) \leq \bigl\lfloor\frac{rn-1}{2}\bigr\rfloor$ and that both bounds are attained for some $r$ and $n$. We prove these conjectured identities for the majority of cases, by defining and characterising selected decompositions of $K_n$. We also provide bounds on $ms_r(G)$ and $cms_r(G)$ as well as results on hypergraph analogues of $ms_r(G)$ and $cms_r(G)$.
Lecture Hall Partitions and the Affine Hyperoctahedral Group
Authors: Hanusa Christopher R. H. , Savage Carla D. 
Published: January 2020

In 1997 Bousquet-Mélou and Eriksson introduced lecture hall partitions as the inversion vectors of elements of the parabolic quotient $\widetilde{C}/C$. We provide a new view of their correspondence that allows results in one domain to be translated into the other. We determine the equivalence between combinatorial statistics in each domain and use this correspondence to translate certain generating function formulas on lecture hall partitions to new observations about $\widetilde{C}/C$.
Cubic Graphs with Small Independence Ratio
Authors: Balogh József , Kostochka Alexandr , Liu Xujun 
Published: January 2020

Let $i(r,g)$ denote the infimum of the ratio $\frac{\alpha(G)}{|V(G)|}$ over the $r$-regular graphs of girth at least $g$, where $\alpha(G)$ is the independence number of $G$, and let $i(r,\infty) := \lim\limits_{g \to \infty} i(r,g)$. Recently, several new lower bounds of $i(3,\infty)$ were obtained. In particular, Hoppen and Wormald showed in 2015 that $i(3, \infty) \geqslant 0.4375,$ and Csóka improved it to $i(3,\infty) \geqslant 0.44533$ in 2016. Bollobás proved the upper bound $i(3,\infty) < \frac{6}{13}$ in 1981, and McKay improved it to $i(3,\infty) < 0.45537$in 1987. There were no improvements since then. In this paper, we improve the upper bound to $i(3,\infty) \leqslant 0.454.$
Transversals, Plexes, and Multiplexes in Iterated Quasigroups
Authors: Taranenko Anna 
Published: January 2020

A $d$-ary quasigroup of order $n$ is a $d$-ary operation over a set of cardinality $n$ such that the Cayley table of the operation is a $d$-dimensional latin hypercube of the same order. Given a binary quasigroup $G$, the $d$-iterated quasigroup $G^{\left[d\right]}$ is a $d$-ary quasigroup that is a $d$-time composition of $G$ with itself. A $k$-multiplex (a $k$-plex) $K$ in a $d$-dimensional latin hypercube $Q$ of order $n$ or in the corresponding $d$-ary quasigroup is a multiset (a set) of $kn$ entries such that each hyperplane and each symbol of $Q$ is covered by exactly $k$ elements of $K$. It is common to call 1-plexes transversals. In this paper we prove that there exists a constant $c(G,k)$ such that if a $d$-iterated quasigroup $G$ of order $n$ has a $k$-multiplex then for large $d$ the number of its $k$-multiplexes is asymptotically equal to $c(G,k) \left(\frac{(kn)!}{k!^n}\right)^{d-1}$. As a corollary we obtain that if the number of transversals in the Cayley table of a $d$-iterated quasigroup $G$ of order $n$ is nonzero then asymptotically it is $c(G,1) n!^{d-1}$. In addition, we provide limit constants and recurrence formulas for the numbers of transversals in two iterated quasigroups of order $5$, characterize a typical $k$-multiplex and estimate numbers of partial $k$-multiplexes and transversals in $d$-iterated quasigroups.
On the Smallest Snarks with Oddness 4 and Connectivity 2
Authors: Goedgebeur Jan 
Published: January 2020

A snark is a bridgeless cubic graph which is not 3-edge-colourable. The oddness of a bridgeless cubic graph is the minimum number of odd components in any 2-factor of the graph.Lukot'ka, Máčajová, Mazák and Škoviera showed in [Electron. J. Combin. 22 (2015)] that the smallest snark with oddness 4 has 28 vertices and remarked that there are exactly two such graphs of that order. However, this remark is incorrect as — using an exhaustive computer search — we show that there are in fact three snarks with oddness 4 on 28 vertices. In this note we present the missing snark and also determine all snarks with oddness 4 up to 34 vertices.
Minimum Number of Additive Tuples in Groups of Prime Order
Authors: Chervak Ostap , Pikhurko Oleg , Staden Katherine 
Published: January 2020

For a prime number $p$ and a sequence of integers $a_0,\dots,a_k\in \{0,1,\dots,p\}$, let $s(a_0,\dots,a_k)$ be the minimum number of $(k+1)$-tuples $(x_0,\dots,x_k)\in A_0\times\dots\times A_k$ with $x_0=x_1+\dots + x_k$, over subsets $A_0,\dots,A_k\subseteq\mathbb{Z}_p$ of sizes $a_0,\dots,a_k$ respectively. We observe that an elegant argument of Samotij and Sudakov can be extended to show that there exists an extremal configuration with all sets $A_i$ being intervals of appropriate length. The same conclusion also holds for the related problem, posed by Bajnok, when $a_0=\dots=a_k=:a$ and $A_0=\dots=A_k$, provided $k$ is not equal 1 modulo $p$. Finally, by applying basic Fourier analysis, we show for Bajnok's problem that if $p\geqslant 13$ and $a\in\{3,\dots,p-3\}$ are fixed while $k\equiv 1\pmod p$ tends to infinity, then the extremal configuration alternates between at least two affine non-equivalent sets.

A corrigendum was added March 12, 2019.
On Certain Edge-Transitive Bicirculants
Authors: Jajcay Robert , Miklavič Štefko , Šparl Primož , Vasiljević Gorazd 
Published: January 2020

A graph $\Gamma$ of even order is a bicirculant if it admits an automorphism with two orbits of equal length. Symmetry properties of bicirculants, for which at least one of the induced subgraphs on the two orbits of the corresponding semiregular automorphism is a cycle, have been studied, at least for the few smallest possible valences. For valences $3$, $4$ and $5$, where the corresponding bicirculants are called generalized Petersen graphs, Rose window graphs and Tabač jn graphs, respectively, all edge-transitive members have been classified. While there are only 7 edge-transitive generalized Petersen graphs and only 3 edge-transitive Tabač jn graphs, infinite families of edge-transitive Rose window graphs exist. The main theme of this paper is the question of the existence of such bicirculants for higher valences. It is proved that infinite families of edge-transitive examples of valence $6$ exist and among them infinitely many arc-transitive as well as infinitely many half-arc-transitive members are identified. Moreover, the classification of the ones of valence $6$ and girth $3$ is given. As a corollary, an infinite family of half-arc-transitive graphs of valence $6$ with universal reachability relation, which were thus far not known to exist, is obtained.
A Notion of Inversion Number Associated to Certain Quiver Flag Varieties
Authors: Fresse Lucas 
Published: January 2020

We define an algebraic variety $X(d,A)$ consisting of matrices whose rows and columns are partial flags. This is a smooth, projective variety, and we describe it as an iterated bundle of Grassmannian varieties. Moreover, we show that $X(d,A)$ has a cell decomposition, in which the cells are parametrized by certain matrices of sets and their dimensions are given by a notion of inversion number. On the other hand, we consider the Spaltenstein variety of partial flags which are stabilized by a given nilpotent endomorphism. We partition this variety into locally closed subvarieties which are affine bundles over certain varieties called $Y_T$, parametrized by semistandard tableaux $T$. We show that the varieties $Y_T$ are in fact isomorphic to varieties of the form $X(d,A)$. We deduce that each variety $Y_T$ has a cell decomposition, in which the cells are parametrized by certain row-increasing tableaux obtained by permuting the entries in the columns of $T$ and their dimensions are given by the inversion number recently defined by P. Drube for such row-increasing tableaux.
The Weighted Davenport Constant of a Group and a Related Extremal Problem
Authors: Balachandran Niranjan , Mazumdar Eshita 
Published: January 2020

For a finite abelian group $G$ written additively, and a non-empty subset $A\subset [1,\exp(G)-1]$ the weighted Davenport Constant of $G$ with respect to the set $A$, denoted $D_A(G)$, is the least positive integer $k$ for which the following holds: Given an arbitrary sequence $(x_1,\ldots,x_k)$ with $x_i\in G$, there exists a non-empty subsequence $(x_{i_1},\ldots,x_{i_t})$ along with $a_{j}\in A$ such that $\sum_{j=1}^t a_jx_{i_j}=0$. In this paper, we pose and study a natural new extremal problem that arises from the study of $D_A(G)$: For an integer $k\ge 2$, determine $f^{(D)}_G(k):=\min\{|A|: D_A(G)\le k\}$ (if the problem posed makes sense). It turns out that for $k$ 'not-too-small', this is a well-posed problem and one of the most interesting cases occurs for $G=\mathbb{Z}_p$, the cyclic group of prime order, for which we obtain near optimal bounds for all $k$ (for sufficiently large primes $p$), and asymptotically tight (up to constants) bounds for $k=2,4$.
The Second Eigenvalue of some Normal Cayley Graphs of Highly Transitive Groups
Authors: Huang Xueyi , Huang Qiongxiang , Cioabă Sebastian M. 
Published: January 2020

Let $G$ be a finite group acting transitively on $[n]=\{1,2,\ldots,n\}$, and let $\Gamma=\mathrm{Cay}(G,T)$ be a Cayley graph of $G$. The graph $\Gamma$ is called normal if $T$ is closed under conjugation. In this paper, we obtain an upper bound for the second (largest) eigenvalue of the adjacency matrix of the graph $\Gamma$ in terms of the second eigenvalues of certain subgraphs of $\Gamma$. Using this result, we develop a recursive method to determine the second eigenvalues of certain Cayley graphs of $S_n$, and we determine the second eigenvalues of a majority of the connected normal Cayley graphs (and some of their subgraphs) of $S_n$ with $\max_{\tau\in T}|\mathrm{supp}(\tau)|\leqslant 5$, where $\mathrm{supp}(\tau)$ is the set of points in $[n]$ non-fixed by $\tau$.
On the Turán Density of $\{1, 3\}$-Hypergraphs
Authors: Bai Shuliang , Lu Linyuan 
Published: January 2020

In this paper, we consider the Turán problems on $\{1,3\}$-hypergraphs. We prove that a $\{1, 3\}$-hypergraph is degenerate if and only if it's $H^{\{1, 3\}}_5$-colorable, where $H^{\{1, 3\}}_5$ is a hypergraph with vertex set $V=[5]$ and edge set $E=\{\{2\}, \{3\}, \{1, 2, 4\},\{1, 3, 5\}, \{1, 4, 5\}\}.$ Using this result, we further prove that for any finite set $R$ of distinct positive integers, except the case $R=\{1, 2\}$, there always exist non-trivial degenerate $R$-graphs. We also compute the Turán densities of some small $\{1,3\}$-hypergraphs.
Diagrams and Essential Sets for Signed Permutations
Authors: Anderson David 
Published: January 2020

We introduce diagrams and essential sets for signed permutations, extending the analogous notions for ordinary permutations. In particular, we show that the essential set provides a minimal list of rank conditions defining the Schubert variety or degeneracy locus corresponding to a signed permutation. Our essential set is in bijection with the poset-theoretic version defined by Reiner, Woo, and Yong, and thus gives an explicit, diagrammatic method for computing the latter.
Rigidity for the Hopf Algebra of Quasisymmetric Functions
Authors: Jia Wanwan , Wang Zhengpan , Yu Houyi 
Published: January 2020

We investigate the rigidity for the Hopf algebra QSym of quasisymmetric functions with respect to the monomial, the fundamental and the quasisymmetric Schur basis, respectively. By establishing some combinatorial properties of the posets of compositions arising from the analogous Pieri rules for quasisymmetric functions, we show that QSym is rigid as an algebra with respect to the quasisymmetric Schur basis, and rigid as a coalgebra with respect to the monomial and the quasisymmetric Schur basis, respectively. The natural actions of reversal, complement and transpose of the labelling compositions lead to some nontrivial graded (co)algebra automorphisms of QSym. We prove that the linear maps induced by the three actions are precisely the only nontrivial graded algebra automorphisms that take the fundamental basis into itself. Furthermore, the complement map on the labels gives the unique nontrivial graded coalgebra automorphism preserving the fundamental basis, while the reversal map on the labels gives the unique nontrivial graded algebra automorphism preserving the monomial basis. Therefore, QSym is rigid as a Hopf algebra with respect to the monomial and the quasisymmetric Schur basis.
Shell Tableaux: A Set Partition Analog of Vacillating Tableaux
Authors: Ly Megan 
Published: January 2020

Schur–Weyl duality is a fundamental framework in combinatorial representation theory. It intimately relates the irreducible representations of a group to the irreducible representations of its centralizer algebra. We investigate the analog of Schur–Weyl duality for the group of unipotent upper triangular matrices over a finite field. In this case, the character theory of these upper triangular matrices is "wild" or unattainable. Thus we employ a generalization, known as supercharacter theory, that creates a striking variation on the character theory of the symmetric group with combinatorics built from set partitions. In this paper, we present a combinatorial formula for calculating a restriction and induction of supercharacters based on statistics of set partitions and seashell inspired diagrams. We use these formulas to create a graph that encodes the decomposition of a tensor space, and develop an analog of Young tableaux, known as shell tableaux, to index paths in this graph.
The Perimeter and Site-Perimeter of Set Partitions
Authors: Mansour Toufik 
Published: January 2020

In this paper, we study the generating function for the number of set partitions of $[n]$ represented as bargraphs according to the perimeter/site-perimeter. In particular, we find explicit formulas for the total perimeter and the total site-perimeter over all set partitions of $[n]$.
Multicolour Bipartite Ramsey Number of Paths
Authors: Bucic Matija , Letzter Shoham , Sudakov Benny 
Published: January 2020

The k$-colour bipartite Ramsey number of a bipartite graph $H$ is the least integer $N$ for which every $k$-edge-coloured complete bipartite graph $K_{N,N}$ contains a monochromatic copy of $H$. The study of bipartite Ramsey numbers was initiated over 40 years ago by Faudree and Schelp and, independently, by Gyárfás and Lehel, who determined the $2$-colour bipartite Ramsey number of paths. Recently the $3$-colour Ramsey number of paths and (even) cycles, was essentially determined as well. Improving the results of DeBiasio, Gyárfás, Krueger, Ruszinkó, and Sárközy, in this paper we determine asymptotically the $4$-colour bipartite Ramsey number of paths and cycles. We also provide new upper bounds on the $k$-colour bipartite Ramsey numbers of paths and cycles which are close to being tight.
Variations on the Petersen Colouring Conjecture
Authors: Pirot François , Sereni Jean-Sébastien , Škrekovski Riste 
Published: January 2020

The Petersen colouring conjecture states that every bridgeless cubic graph admits an edge-colouring with 5 colours such that for every edge e, the set of colours assigned to the edges adjacent to e has cardinality either 2 or 4, but not 3. We prove that every bridgeless cubic graph $G$ admits an edge-colouring with 4 colours such that at most $8/15\cdot|E(G)|$ edges do not satisfy the above condition. This bound is tight and the Petersen graph is the only connected graph for which the bound cannot be decreased. We obtain such a 4-edge-colouring by using a carefully chosen subset of edges of a perfect matching, and the analysis relies on a simple discharging procedure with essentially no reductions and very few rules.
On Orthogonal Symmetric Chain Decompositions
Authors: Däubel Karl , Jäger Sven , Mütze Torsten , Scheucher Manfred 
Published: January 2020

The $n$-cube is the poset obtained by ordering all subsets of $\{1,\ldots,n\}$ by inclusion, and it can be partitioned into $\binom{n}{\lfloor n/2\rfloor}$ chains, which is the minimum possible number. Two such decompositions of the $n$-cube are called orthogonal if any two chains of the decompositions share at most a single element. Shearer and Kleitman conjectured in 1979 that the $n$-cube has $\lfloor n/2\rfloor+1$ pairwise orthogonal decompositions into the minimum number of chains, and they constructed two such decompositions. Spink recently improved this by showing that the $n$-cube has three pairwise orthogonal chain decompositions for $n\geq 24$. In this paper, we construct four pairwise orthogonal chain decompositions of the $n$-cube for $n\geq 60$. We also construct five pairwise edge-disjoint symmetric chain decompositions of the $n$-cube for $n\geq 90$, where edge-disjointness is a slightly weaker notion than orthogonality, improving on a recent result by Gregor, Jäger, Mütze, Sawada, and Wille.
The Maximum Number of Cycles in a Graph with Fixed Number of Edges
Authors: Arman Andrii , Tsaturian Sergei 
Published: January 2020

The main problem considered in this paper is maximizing the number of cycles in a graph with given number of edges. In 2009, Király conjectured that there is constant $c$ such that any graph with $m$ edges has at most $c(1.4)^m$ cycles. In this paper, it is shown that for sufficiently large $m$, a graph with $m$ edges has at most $(1.443)^m$ cycles. For sufficiently large $m$, examples of a graph with $m$ edges and $(1.37)^m$ cycles are presented. For a graph with given number of vertices and edges an upper bound on the maximal number of cycles is given. Also, bounds tight up to a constant are presented for the maximum number of cycles in a multigraph with given number of edges, as well as in a multigraph with given number of vertices and edges.
Evaluasi Pilkada Serentak 2015 dan Pemilu 2019: Sebuah Catatan Singkat
Authors: Warganegara Arizka 
Published: January 2020

Indikator sebuah negara demokrasi selalu diawali dengan adanya pemilihan umum, baik dilevel nasional maupun lokal. Pelaksaan Pilkada serentak tahun 2015 dan Pemilu tahun 2019 mengindikasi bahwa Indonesia sudah menjadi negara yang bergerak menuju negara dengan demokrasi yang matang. Sejauh ini tidak ditemukan konflik yang mengakar diaras public walaupun perhelatan dua event demokrasi besar tersebit menyisakan beragam evaluasi dimulai dari kritik terhadap sistem pemilu yang terlalu rumit, penyelenggara yang belum sempurna mengejahwantahkan peraturan pemilu di lapangan, kekurangan logistik pemilu dan berbagai pelanggaran pemilu yang ditemukan. Tulisan ini mencoba memberikan catatan terhadap kedua event politik tersebut. Catatan yang paling utama bagi Pilkada serentak adalah potensi kecurangan ternyata bukan terletak pada biaya kampanye formal yang pada Pilkada 2015 ditanggung oleh ‘penyelenggara’, dalam konteks ini penyelenggara harus mampu menemukan formulasi teknis yang dapat mengurangi sebaran politik uang dan hal itu akan lebih bermanfaat bagi kualitas pemimpin yang terpilih. Sedangkan bagi Pemilu 2019, saya melihat justru persoalan distribusi logistic, pendataan pemilih dan sistem pemilu proporsional terbuka menjadi hal utama yang harus menjadi catatan dalam evaluasi Pemilu 2019.
A Fireball and Potentially Hazardous Binary Near-Earth Asteroid (164121) 2003 YT1
Authors: Kasuga Toshihiro , Sato Mikiya , Ueda Masayoshi , Fujiwara Yasunori , Tsuchiya Chie , Watanabe Jun-ichi 
Published: January 2020

Abstract
We present a fireball detected in the night sky over Kyoto, Japan on UT 2017 April 28 at

by the SonotaCo Network. The absolute visual magnitude is

= −4.10 ± 0.42 mag. Luminous light curves obtain a meteoroid mass of m = 29 ± 1 g, corresponding to the size of a
s = 2.7 ± 0.1 cm. Orbital similarity assessed by D-criterions (see D
SH = 0.0079) has identified a likely parent, the binary near-Earth asteroid (164121) 2003 YT1. The suggested binary formation process is a Yarkovsky–O’Keefe–Radzievskii–Paddack-driven rotational disintegration. The asynchronous state indicates the age of <104 yr, near or shorter than the upper limit to meteoroid stream lifetime. We examine potential dust production mechanisms for the asteroid, including rotational instability, resurfacing, impact, photoionization, radiation pressure sweeping, thermal fracture, and sublimation of ice. We find some of them capable of producing the meteoroid-scale particles. Rotational instability is presumed to cause mass shedding, in consideration of the recent precedents (e.g., asteroid (6478) Gault), possibly releasing millimeter–centimeter scale dust particles. Impacts by micrometeorites with a size ≃1 mm could be a trigger for ejecting the centimeter-sized particles. Radiation pressure can sweep out the millimeter-sized dust particles, while not sufficient for the centimeter-sized. The other mechanisms are unprovable or unidentified. The feasibility in the parental aspect of 2003 YT1 is somewhat reconciled with the fireball observation, yielding an insight into how we approach potentially hazardous objects.
Tidally Excited Oscillations in Heartbeat Binary Stars: Pulsation Phases and Mode Identification
Authors: Guo Zhao , Shporer Avi , Hambleton Kelly , Isaacson Howard 
Published: January 2020

Abstract
Tidal forces in eccentric binary stars known as heartbeat stars excite detectable oscillations that shed light on the processes of tidal synchronization and circularization. We examine the pulsation phases of tidally excited oscillations (TEOs) in heartbeat binary systems. The target list includes four published heartbeat binaries and four additional systems observed by Kepler. To the first order, the pulsation phases of TEOs can be explained by the geometric effect of the dominant l = 2, m = 0, or ±2 modes assuming pulsations are adiabatic. We found that this simple theoretical interpretation can account for more than half of the systems on the list, assuming their spin and orbit axes are aligned. We do find significant deviations from the adiabatic predictions for some other systems, especially for the misaligned binary KIC 8164262. The deviations can potentially help to probe the nonadiabaticity of pulsation modes as well as resonances in the tidal forcing.