76 citations · 143 across the 12 of their papers we have counts for
13 papers
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…
From the Fundamental Theorem of Algebra to Kempe's Universality Theorem
Gábor Hegedüs, Zijia Li, Josef Schicho +1
This article provides a gentle introduction for a general mathematical audience to the factorization theory of motion polynomials and its application in mechanism science. This the…
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…
The Theory of Bonds II: Closed 6R Linkages with Maximal Genus
Gábor Hegedüs, Zijia Li, Josef Schicho +1
In this paper, we introduce a method that allows to produce necessary conditions on the Denavit--Hartenberg parameters for the mobility of a closed linkage with six rotational join…
The Theory of Bonds: A New Method for the Analysis of Linkages
Gábor Hegedüs, Josef Schicho, Hans-Peter Schröcker
In this paper we introduce a new technique, based on dual quaternions, for the analysis of closed linkages with revolute joints: the theory of bonds. The bond structure comprises a…
Factorization of Rational Curves in the Study Quadric and Revolute Linkages
Gábor Hegedüs, Josef Schicho, Hans-Peter Schröcker
Given a generic rational curve in the group of Euclidean displacements we construct a linkage such that the constrained motion of one of the links is exactly . Our construct…
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…