4 papers
math.CO2023
Variations on the Bollobás set-pair theorem
Gábor Hegedüs, Péter Frankl
Let be an -element set. A set-pair system $\mbox{$\cal P$}=\{(A_i,B_i)\}_{1\leq i\leq m}$ is a collection of pairs of disjoint subsets of . It is called skew Bollobás sys…
math.CO2023
Upper bounds for the size of set systems with a symmetric set of Hamming distances
Gábor Hegedüs
Let $\mbox{$\cal F$}\subseteq 2^{[n]}$ be a fixed family of subsets. Let $D(\mbox{$\cal F$})$ stand for the following set of Hamming distances: $$ D(\mbox{}):=\{d_H(F,G):~…
math.CO2022
Gröbner Bases for Increasing Sequences
Gábor Hegedüs, Lajos Rónyai
Let be integers, , and be a field with . The set of increasing sequences $$ I(n,q)=\{(f_1,f_2, \dots, f_n) \in [q]^…
math.CO2018
A generalization of Croot-Lev-Pach's Lemma and a new upper bound for the size of difference sets in polynomial rings
Gábor Hegedüs
Croot, Lev and Pach used a new polynomial technique to give a new exponential upper bound for the size of three-term progression-free subsets in the groups . The…