76 citations · 143 across the 12 of their papers we have counts for
9 papers · 1 filter
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…
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: $$ D(\mbox{}):=\{d_H(F,G):~…
Gröbner Bases for Increasing Sequences
Gábor Hegedüs, Lajos Rónyai
Let be integers, , and be a field with . The set of increasing sequences $$ I(n,q)=\{(f_1,f_2, \dots, f_n) \in [q]^…
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…
A generalization of the Erdős-Ko-Rado Theorem
Gábor Hegedüs
Our main result is a new upper bound for the size of k-uniform, L-intersecting families of sets, where L contains only positive integers. We characterize extremal families in this…
Ehrhart polynomial roots of reflexive polytopes
Gábor Hegedüs, Akihiro Higashitani, Alexander Kasprzyk
Recent work has focused on the roots z of the Ehrhart polynomial of a lattice polytope P. The case when Re(z) = -1/2 is of particular interest: these polytopes satisfy Golyshev's "…
An explicit Ramsey graph
Gábor Hegedüs
Explicit construction of Ramsey graphs has remained a challenging open problem for a long time. Frankl--Wilson \cite{FW}, Alon \cite{A} and Grolmusz \cite{G2} gave the best explici…
Multivalued generalizations of the Frankl--Pach Theorem
Gabor Hegedüs, Lajos Ronyai
P. Frankl and J. Pach proved the following uniform version of Sauer's Lemma. Let be natural numbers such that , . Let $\cF \subseteq {[n] \choose d}$…
Roots of Ehrhart Polynomials of Smooth Fano Polytopes
Gábor Hegedüs, Alexander M. Kasprzyk
V. Golyshev conjectured that for any smooth polytope P of dimension at most five, the roots $z\in\C$ of the Ehrhart polynomial for P have real part equal to -1/2. An elementary pro…