47 articles in this issue
Pierre Aboulker, Guillaume Aubian, Chien-Chung Huang
David G. Harris
The Lopsided Lovász Local Lemma (LLLL) is a probabilistic tool which is a cornerstone of the probabilistic method of combinatorics, which shows that it is possible to avoid a collection of "bad" events as long as their probabilities and interdependencies ... see more
Maxime Pelletier, Nicolas Ressayre
Deepesh Singhal, Yuxin Lin
Oliver Cooley, Mihyun Kang, Julian Zalla
Abdul Basit, Daniel McGinnis, Henry Simmons, Matt Sinnwell, Shira Zerbib
Vuong Bui
Kolja Knauer, Hoang La, Petru Valicov
Alvaro Carbonero, Willem Fletcher, Jing Guo, András Gyárfás, Rona Wang, Shiyu Yan
A 3-graph is a pair H = (V, E) of sets, where elements of V are called points or vertices and E contains some 3-element subsets of V , called edges. A 3-graph is called linear if any two distinct edges intersect in at most one vertex.There is a recent int... see more
On-Hei Solomon Lo
The prism over a graph GG is the Cartesian product of GG with the complete graph K2K_2. The graph GG is prism-hamiltonian if the prism over GG has a Hamilton cycle. A good even cactus is a connected graph in which every block is either an edge or an even ... see more
Marija Dodig, Marko Stosic
In this paper, we give a complete, explicit and constructive solution to the double generalized majorization problem. Apart from purely combinatorial interest, double generalized majorization problem has strong impact in Matrix and Matrix Pencils Completi... see more
Yongtao Li, Yuejian Peng
Kathy Q. Ji, Dax T.X. Zhang
We introduce the cyclic major index of a cyclic permutation and give a bivariate analogue of the enumerative formula for the cyclic shuffles with a given cyclic descent number due to Adin, Gessel, Reiner and Roichman, which can be viewed as a cyclic analo... see more
Alex M. Kodess, Brian G. Kronenthal, Tony W.H. Wong
For a field F\mathbb{F} and functions f,g,h,j:F?Ff,g,h,j\colon\mathbb{F}\to \mathbb{F}, we define GF(f(X)h(Y),g(X)j(Y))\Gamma_\mathbb{F}(f(X)h(Y),g(X) j(Y)) to be a bipartite graph where each partite set is a copy of F3\mathbb{F}^3, and a vertex (a,a2,a3)... see more
Guido Brückner, Ignaz Rutter, Peter Stumpf
Fulek et al. (2013, 2016, 2017) have presented Hanani-Tutte results for (radial) level-planarity, i.e., a graph is (radial) level-planar if it admits a (radial) level drawing where any two independent edges cross an even number of times. We show that the&... see more
Oliver Bachtler, Sven O. Krumke
Alperen Özdemir
Andrew R. Conway, Miles Conway, Andrew Elvey Price, Anthony J. Guttmann
Zachary DeStefano, Hannah Mahon, Frank Simutis, Michael Tait
Boris Bukh, Ting-Wei Chao
Digital nets (in base 2) are the subsets of [0,1]d that contain exactly the expected number of points in every not-too-small dyadic box. We construct finite sets, which we call "almost nets", such that every such dyadic box contains almost the expected nu... see more
Stephen R. Doty
Jakub Pekárek, Jean-Sébastien Sereni, Zelealem B. Yilma
Jorge Neves, Gonçalo Varejão
We define the Eulerian ideal of a kk-uniform hypergraph and study its degree and Castelnuovo-Mumford regularity. The main tool is a Gröbner basis of the ideal obtained combinatorially from the hypergraph. We define the notion of parity join in a hypergrap... see more
Ján Mazák, Jozef Rajník, Martin Škoviera
Cameron Crenshaw, James Oxley
The cycles of a graph give a natural cyclic ordering to their edge-sets, and these orderings are consistent in that two edges are adjacent in one cycle if and only if they are adjacent in every cycle in which they appear together. An orderable matroid is ... see more
Mathilde Bouvel, Lapo Cioni, Luca Ferrari
Shamil Asgarli, Sergey Goryainov, Huiqiu Lin, Chi Hoi Yip
We prove that a family of pseudo-Paley graphs of square order obtained from unions of cyclotomic classes satisfies the Erdos-Ko-Rado (EKR) module property, in a sense that the characteristic vector of each maximum clique is a linear combination of charact... see more
Dibyayoti Dhananjay Jena
Arnbjörg Soffía Árnadóttir, Waltraud Lederle, Rögnvaldur G. Möller
We study groups acting vertex-transitively and non-discretely on connected, cubic graphs (regular graphs of degree 3). Using ideas from Tutte's fundamental papers in 1947 and 1959, it is shown that if the action is edge-transitive, then the graph has to b... see more
Sophie Rehberg
Generalized permutahedra are a class of polytopes with many interesting combinatorial subclasses. We introduce pruned inside-out polytopes, a generalization of inside-out polytopes introduced by Beck-Zaslavsky (2006), which have many applications such as ... see more
Letong Hong, Rupert Li
Dennis Eichhorn, Lydia Engle, Brandt Kronholm
In this paper, we establish infinite families of congruences in consecutive arithmetic progressions modulo any odd prime l\ell for the function p(n,m,N)p\big(n,m,N\big), which enumerates the partitions of nn into at most mm parts with no part larger than ... see more
Farid Aliniaeifard, Nathaniel Thiem
Combinatorial Hopf algebras give a linear algebraic structure to infinite families of combinatorial objects, a technique further enriched by the categorification of these structures via the representation theory of families of algebras. This paper e... see more
Alvaro Carbonero, Patrick Hompe, Benjamin Moore, Sophie Spirkl
For t=2t \ge 2, let us call a digraph DD t-chordal if all induced directed cycles in DD have length equal to tt. In an earlier paper, we asked for which tt it is true that tt-chordal graphs with bounded clique number have bounded dichromatic number. Recen... see more
Paul-Henry Leemann, Mikael de la Salle
If GG is a group and SS a generating set, GG canonically embeds into the automorphism group of its Cayley graph and it is natural to try to minimize, over all generating sets, the index of this inclusion. This infimum is called the Cayley index of the gro... see more
Guorong Gao, An Chang
An rr-uniform hypergraph is linear if every two edges intersect in at most one vertex. Given a family of rr-uniform hypergraphs F\mathcal{F}, the linear Turán number exlinr(n,F)_r^{lin}(n,\mathcal{F}) is the maximum number of edges of a linear rr-uniform ... see more
Bérénice Delcroix-Oger, Matthieu Josuat-Vergès, Lucas Randazzo
In 1980, Edelman defined a poset on objects called the noncrossing 2-partitions. They are closely related with noncrossing partitions and parking functions. To some extent, his definition is a precursor of the parking space theory, in the framework of fin... see more
Yosef Berman, Bridget Eileen Tenner
We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern counts, both in ter... see more
Zequn Lv, Mei Lu, Chunqiu Fang
Let CkC_k be a cycle of order kk, where k=3k\ge 3. Let ex(n,n,n,{C3,C4})(n, n, n, \{C_{3}, C_{4}\}) be the maximum number of edges in a balanced 33-partite graph whose vertex set consists of three parts, each has nn vertices that has no subgraph isomorphi... see more
Raphael Yuster
Let HH be a directed acyclic graph (dag) that is not a rooted star. It is known that there are constants c=c(H)c=c(H) and C=C(H)C=C(H) such that the following holds for DnD_n, the complete directed graph on nn vertices. There is a set of at most ClognC\lo... see more
Bart De Bruyn
Jianbing Liu, Miaomiao Han, Hong-Jian Lai
Given a graph GG and an odd prime pp, for a mapping f:E(G)?Zp\{0}f: E(G) \to {\mathbb Z}_p\setminus\{0\} and a Zp{\mathbb Z}_p-boundary bb of GG, an orientation t\tau is called an (f,b;p)(f,b;p)-orientation if the net out ff-flow is the same as b(v)b(v) i... see more
Maciej Dolega, Maciej Kowalski
So-Yeon Lee, Young-Tak Oh
Amanda Welch
We classify cocovers of a given element of the double affine Weyl semigroup WTW_{\mathcal{T}} with respect to the Bruhat order, specifically when WTW_{\mathcal{T}} is associated to a finite root system that is irreducible and simply laced. We do so by int... see more
Shuya Chiba, Michitaka Furuya
Marcelo Garlet Millani, Raphael Steiner, Sebastian Wiederrecht