The EKR-module property of pseudo-Paley graphs of square order

Peisert型图中的Erdős-Ko-Rado定理

Erdős-Ko-Rado theorem in Peisert-type graphs

本研究针对Peisert型图中的EKR定理问题，证明Paley图的EKR定理可推广到几乎所有Peisert型伪Paley图，并建立了同类稳定性结果，拓展了该定理的适用范围。

不具有严格EKR性质的极值Peisert型图

Extremal Peisert-type graphs without the strict-EKR property

本研究针对不具有严格EKR性质的边数最少的极值Peisert型图，确定了各素数幂q对应的边数，证明平方或立方q下极值图的唯一性并分类最大团，还验证了平方q下的相关界的紧性。

The EKR property for flag pure simplicial complexes without boundary

We prove that the family of facets of a pure simplicial complex of dimension up to three satisfies the Erdős-Ko-Rado property whenever it is flag and has no boundary ridges. We conjecture the same to be true in arbitrary dimension and give evidence for this conjecture. Our motivation is that complexes with these two properties include flag pseudo-manifolds and cluster complexes.

A Paley-like graph in characteristic two

The Paley graph is a well-known self-complementary pseudo-random graph, defined over a finite field of odd order. We describe an attempt at an analogous construction using fields of even order. Some properties of the graph are noted, such as the existence of a Hamiltonian decomposition.

来自分圆类并的伪佩利图中最大团的子空间结构

The subspace structure of maximum cliques in pseudo-Paley graphs from unions of cyclotomic classes

本文研究由半本原分圆类并构成的伪佩利图中具子空间结构的√q大小团的存在性，证明这类团需各分圆类贡献相等且多数伪佩利图无此类团，还证实广义佩塞特图与佩利图、佩塞特图不同构。

Spectral pseudorandomness and the road to improved clique number bounds for Paley graphs

We study subgraphs of Paley graphs of prime order $p$ induced on the sets of vertices extending a given independent set of size $a$ to a larger independent set. Using a sufficient condition proved in the author's recent companion work, we show that a family of character sum estimates would imply that, as $p \to \infty$, the empirical spectral distributions of the adjacency matrices of any sequence of such subgraphs have the same weak limit (after rescaling) as those of subgraphs induced on a random set including each vertex independently with probability $2^{-a}$, namely, a Kesten-McKay law wi…