Electronic Journal of Combinatorics  

José Aliste-Prieto, Logan Crew, Sophie Spirkl, José Zamora

This paper has two main parts. First, we consider the Tutte symmetric function XB, a generalization of the chromatic symmetric function. We introduce a vertex-weighted version of XB and show that this function admits a deletion-contraction relation. We al... see more

Jordan Mitchell Barrett

We further develop the theory of layered semigroups, as introduced by Farah, Hindman and McLeod, providing a general framework to prove Ramsey statements about such a semigroup SS. By nonstandard and topological arguments, we show Ramsey statements on SS ... see more

Kasper Szabo Lyngsie, Liang Zhong

Kayla Bell, Keith Driscoll, Elliot Krop, Kimber Wolff

Victor A. Campos, Guilherme C.M. Gomes, Allen Ibiapina, Raul Lopes, Ignasi Sau, Ana Silva

Adam Burchardt

Jesse Geneson

Arnfried Kemnitz, Margit Voigt

Jesús Salas, Alan D. Sokal

Mark Skandera

Michael Albert, Murray Tannock

Maria Chudnovsky, Shenwei Huang, T. Karthick, Jenny Kaufmann

Yuanqiu Huang, Zhangdong Ouyang, Fengming Dong

Lyuben Lichev

Burkill and Mirsky, and Kalmanson prove independently that, for every r=2,n=1r\ge 2, n\ge 1, there is a sequence of r2nr^{2^n} vectors in Rn\mathbb R^n, which does not contain a subsequence of r+1r+1 vectors v1,v2,…,vr+1v^1, v^2,\dots,v^{r+1} such that, f... see more

Jeffrey A. Mudrock, Seth Thomason

Bin Chen, An Chang

In 2019, Czabarka, Dankelmann and Székely showed that for every undirected graph of order nn, the minimum degree threshold for diameter two orientability is n2+T(lnn)\frac{n}{2}+ \Theta(\ln n). In this paper, we consider bipartite graphs and give a suffic... see more

Max Hahn-Klimroth, Giulia S. Maesaka, Yannick Mogge, Samuel Mohr, Olaf Parczyk

Pierre Aboulker, Pierre Charbit, Reza Naserasr

Brent Holmes, Justin Lyle

We prove some new rank selection theorems for balanced simplicial complexes. Specifically, we prove that if a balanced simplicial complex satisfies Serre's condition (Sl)(S_{\ell}) then so do all of its rank selected subcomplexes.  We also provide a ... see more

João Miguel Santos

We compute, mimicking the Lascoux-Schützenberger type A combinatorial procedure, left and right keys for a Kashiwara-Nakashima tableau in type C. These symplectic keys have a similar role as the keys for semistandard Young tableaux. More precisely, our sy... see more

James Aaronson, David Ellis, Imre Leader

We show that the Union-Closed Conjecture holds for the union-closed family generated by the cyclic translates of any fixed set.

Jia Huang

The Norton product is defined on each eigenspace of a distance regular graph by the orthogonal projection of the entry-wise product. The resulting algebra, known as the Norton algebra, is a commutative nonassociative algebra that is useful in group theory... see more

Michael Anastos, Ander Lamaison, Raphael Steiner, Tibor Szabó

Nursel Erey, Takayuki Hibi

Let I(G)[k]I(G)^{[k]} denote the kkth squarefree power of the edge ideal of GG. When GG is a forest, we provide a sharp upper bound for the regularity of I(G)[k]I(G)^{[k]} in terms of the kk-admissable matching number of GG. For any positive integer kk, w... see more

Beata Casiday, Selvi Kara

Let D\mathcal{D} be a weighted oriented graph and I(D)I(\mathcal{D}) be its edge ideal. In this paper, we investigate the Betti numbers of I(D)I(\mathcal{D}) via upper-Koszul simplicial complexes, Betti splittings and the mapping cone construction. In par... see more

Ravi B. Boppana, Harrie Hendriks, Martien C.A. van Zuijlen

Let v1,v2,…,vnv_1,v_2,\ldots, v_n be real numbers whose squares add up to 1.  Consider the 2n2^n signed sums of the form S=?±viS = \sum \pm v_i.  Boppana and Holzman (2017) proved that at least 13/32 of these sums satisfy |S|=1|S| \le 1.  H... see more

Svante Janson, Wojciech Szpankowski

Charlotte Knierim, Maxime Larcher, Anders Martinsson

Camille Combe

George Drummond, Zach Gershkoff, Susan Jowett, Charles Semple, Jagdeep Singh

Zhiyang He

In this paper, we prove ex(n,C2k)=(16v5vklogk+o(1))·n1+1/k\mathrm{ex}(n, C_{2k})\le (16\sqrt{5}\sqrt{k\log k} + o(1))\cdot n^{1+1/k}. This improves on a result of Bukh and Jiang from 2017, thereby reducing the best known upper bound by a factor of v5logk\... see more

Zoltán Füredi, Ruth Luo

Qinghou Zeng, Chunlei Zu

In this paper, we consider the decomposition of multigraphs under minimum degree constraints and give a unified generalization of several results by various researchers. Let GG be a multigraph in which no quadrilaterals share edges with triangles and othe... see more

Reza Naserasr, Zhouningxin Wang, Xuding Zhu

Margaret Bayer, Bennet Goeckner, Su Ji Hong, Tyrrell McAllister, McCabe Olsen, Casey Pinckney, Julianne Vega, Martha Yip

Given a family of lattice polytopes, two common questions in Ehrhart Theory are determining when a polytope has the integer decomposition property and determining when a polytope is reflexive. While these properties are of independent interest, the conflu... see more

Gohar Kyureghyan, Shuxing Li, Alexander Pott

The intersection distribution of a polynomial ff over finite field Fq\mathbb{F}_q was recently proposed by Li and Pott [\emph{Finite Fields and Their Applications, 66 (2020)}], which concerns the collective behaviour of a collection of polynomials {f(x)+c... see more

N. R. Aravind, Stijn Cambie, Wouter Cames van Batenburg, Rémi de Joannis de Verclos, Ross J. Kang, Viresh Patel

Niranjan Balachandran, Deepanshu Kush

A bipartite graph G(X,Y,E)G(X,Y,E) with vertex partition (X,Y)(X,Y) is said to have the Normalized Matching Property (NMP) if for any subset S?XS\subseteq X we have |N(S)||Y|=|S||X|\frac{|N(S)|}{|Y|}\geq\frac{|S|}{|X|}. In this paper, we prove the followi... see more

Colin Defant, Andrew Elvey Price, Anthony J. Guttmann

Timothy Y. Chow, Jennifer Paulhus

Suppose that ??\chi_\lambda and ?µ\chi_\mu are distinct irreducible characters of the symmetric group SnS_n. We give an algorithm that, in time polynomial in nn, constructs p?Sn\pi\in S_n such that ??(p)\chi_\lambda(\pi) is provably different from ?µ(p)\c... see more

Adam Doliwa

We introduce a coloured generalization  NSymA\mathrm{NSym}_A of the Hopf algebra of non-commutative symmetric functions  described as a subalgebra of the of rooted ordered coloured trees Hopf algebra. Its natural basis can be identified with the... see more

Grant T. Barkley, Ricky Ini Liu

Let mGm_G denote the number of perfect matchings of the graph GG. We introduce a number of combinatorial tools for determining the parity of mGm_G and giving a lower bound on the power of 2 dividing mGm_G. In particular, we introduce certain vertex sets c... see more

Julien Courtiel, Andrew Elvey Price, Irène Marcovici

This paper solves an open question of Mortimer and Prellberg asking for an explicit bijection between two families of walks. The first family is formed by what we name triangular walks, which are two-dimensional walks moving in six directions (0°, 60°, 12... see more

Peter Frankl, Andrey Kupavskii

Let n>k>1n > k > 1 be integers, [n]={1,…,n}[n] = \{1, \ldots, n\}. Let F\mathcal F be a family of kk-subsets of [n][n]. The family F\mathcal F is called intersecting if FnF'?ØF \cap F' \neq \varnothing for all F,F'?FF, F' \in \mathcal F. It is calle... see more

Carl Johan Casselgren, Lan Anh Pham

Given a partial edge coloring of a complete graph KnK_n and lists of allowed colors for the non-colored edges of KnK_n, can we extend the partial edge coloring to a proper edge coloring of KnK_n using only colors from the lists? We prove that this questio... see more

Jaehoon Kim, Sang-il Oum