G. Hegedus

activity

20102023

most citedThe boundary volume of a lattice polytope

4 citations · 8 across the 15 of their papers we have counts for

collaborators

21 papers

math.CO2023

Non-uniform skew versions of Bollobás' Theorem

Gábor Hegedüs

Let $A_{1}, \dots, A_{m}$ and $B_{1}, \dots, B_{m}$ be subsets of $[n]$ and let $t$ be a non-negative integer with the following property: $∣ A_{i} \cap B_{i} ∣ \leq t$ for each $i$ and $|A_i\c…

math.CO2021

An uniform version of Dvir and Moran's theorem

Gábor Hegedüs

Dvir and Moran proved the following upper bound for the size of a family $\mbox{$\cal F$}$ of subsets of $[n]$ with $\mbox{Vdim}(\mbox{$\cal F$} Δ\mbox{$\cal F$})\leq d$. Let $d\le…

math.CO2021

$L$ -balancing families

Gábor Hegedüs

P. Hrube\v s, S. Natarajan Ramamoorthy, A. Rao and A. Yehudayoff proved the following result: Let $p$ be a prime and let $f \in F_{p} [x_{1}, \dots, x_{2 p}]$ be a polynomial. Sup…

math.NT2020

Sets avoiding $p$ -term arithmetic progressions in $Z_{q}^{n}$ are exponentially small

Gábor Hegedüs

Pach and Palincza proved the following generalization of Ellenberg and Gijswijt's bound for the size of $k$ -term arithmetic progression-free subsets, where $k \in {4, 5, 6}$ : Let $m…

math.CO2020

A new proof of a generalization of Gerzon's bound

Gábor Hegedüs

In this paper we give a short, new proof of a natural generalization of Gerzon's bound. This bound improves the Delsarte, Goethals and Seidel's upper bound in a special case. Our p…

math.CO2018

A new upper bound for the size of $s$ -distance sets in boxes

Gábor Hegedüs

Let $q, d \geq 2$ be integers. Define $J (q, d) := \frac{1}{q} (0 < x < 1 min \frac{1 - x ^{q}}{1 - x} x^{- \frac{q - 1}{d}}) .$ Let $\mbox{$\cal G$}\subseteq {\mathbb R}^n$ be an arbitrar…

math.NT2017

A new exponential upper bound for the Erdős-Ginzburg-Ziv constant

Gábor Hegedüs

Naslund used Tao's slice rank bounding method to give new exponential upper bounds for the Erdős--Ginzburg-Ziv constant of finite Abelian groups of high rank. In our short manuscri…

math.CO2017

A note on linear Sperner families

Gábor Hegedüs, Lajos Rónyai

In an earlier work we described Gröbner bases of the ideal of polynomials over a field, which vanish on the set of characteristic vectors $v \in {0, 1}^{n}$ of the complete…

math.CO2016

Inequalities for two systems of subspaces with prescribed intersections

Gábor Hegedüs

Let $W$ denote a linear space over a fixed field $F$ . We define the notions of weak $I S P$ -system and weak $(u, v)$ -system $S = {(U_{i}, V_{i}) : 1 \leq i \leq m}$ of subspac…

math.CO2015

A Bollobás-type theorem for affine subspaces

Gábor Hegedüs

Let $W$ denote the $n$ -dimensional affine space over the finite field $F_{q}$ . We prove here a Bollobás-type upper bound in the case of the set of affine subspaces. We give a…

math.CO2015

Shattering bounds for tuple systems

Gábor Hegedüs

Let $\mbox{ V}(n,d,q)$ stand for the $q$ --ary Hamming spheres. Let $\mbox{ C}\subseteq (q)^n$ denote a tuple system such that $\mbox{ C}\subseteq \cup_{i=0}^s \mbox{ V}(n,d_i,q)$,…

math.CO2014

Let $n$ be an arbitrary integer, let $p$ be a prime factor of $n$ . Denote by $ω_{1}$ the $p^{t h}$ primitive unity root, $ω_{1} := e^{\frac{2 π i}{p}}$ . Define $ω_{i} := ω_{1}^{i}$ for $0\leq i\leq…

math.CO2011

An Upper Bound Theorem concerning lattice polytopes

Gabor Hegedüs

R. P. Stanley proved the Upper Bound Conjecture in 1975. We imitate his proof for the Ehrhart rings. We give some upper bounds for the volume of integrally closed lattice polytopes…

math.AC2011

Betti numbers of Stanley--Reisner rings with pure resolutions

Gabor Hegedüs

Let $Δ$ be simplicial complex and let $k [Δ]$ denote the Stanley--Reisner ring corresponding to $Δ$ . Suppose that $k [Δ]$ has a pure free resolution. Then we describe the Betti numbe…

math.AC2011

The $f$ --vector of the clique complex of chordal graphs and Betti numbers of edge ideals of uniform hypergraphs

Gabor Hegedüs

We describe the Betti numbers of the edge ideals $I (G)$ of uniform hypergraphs $G$ such that $I (G)$ has linear graded free resolution. We give an algebraic equation system and some…

math.MG2010

The Minkowskian planar 4R mechanism

Gabor Hegedüs, Brian Moore

We characterize and classify completely the planar 4R closed chain working on the Minkowskian plane. Our work would open a new research direction in the theory of geometric designs…

math.CO2010★ 3 cited

Betti numbers of Stanley--Reisner rings with pure resolutions

Gabor Hegedüs

Let $Δ$ be simplicial complex and let $k [Δ]$ denote the Stanley--Reisner ring corresponding to $Δ$ . Suppose that $k [Δ]$ has a pure free resolution. Then we describe the Betti numbe…

math.CO2010★ 1 cited

The surface of a lattice polytope

Gábor Hegedüs

My main results are simple formulas for the surface area of d-dimensional lattice polytopes using Ehrhart theory.

math.CO2010

The number of permutations with k inversions

Gábor Hegedüs

Let $n \geq 1$ , $0 \leq t \leq (2 n)$ be arbitrary integers. Define the numbers $I_{n} (t)$ as the number of permutations of $[n]$ with $t$ inversions. Let $n, d \geq 1$ and $0\leq…

math.AC2010

Linear equations for the number of intervals which are isomorphic with Boolean lattices and the Dehn--Sommerville equations

Gábor Hegedüs

Let $P$ be a finite poset. Let $L := J (P)$ denote the lattice of order ideals of $P$ . Let $b_{i} (L)$ denote the number of Boolean intervals of $L$ of rank $i$ . We construct a simple gr…

math.CO2010★ 4 cited

The boundary volume of a lattice polytope

Gábor Hegedüs, Alexander M. Kasprzyk

For a d-dimensional convex lattice polytope P, a formula for the boundary volume is derived in terms of the number of boundary lattice points on the first $\floor{d/2}$ dilations o…

Non-uniform skew versions of Bollobás' Theorem

An uniform version of Dvir and Moran's theorem

L-balancing families

Sets avoiding p-term arithmetic progressions in Zqn​ are exponentially small

A new proof of a generalization of Gerzon's bound

A new upper bound for the size of s-distance sets in boxes

A new exponential upper bound for the Erdős-Ginzburg-Ziv constant

A note on linear Sperner families

Inequalities for two systems of subspaces with prescribed intersections

A Bollobás-type theorem for affine subspaces

Shattering bounds for tuple systems

Balancing Sets of Vectors

An Upper Bound Theorem concerning lattice polytopes

Betti numbers of Stanley--Reisner rings with pure resolutions

The f--vector of the clique complex of chordal graphs and Betti numbers of edge ideals of uniform hypergraphs

The Minkowskian planar 4R mechanism

Betti numbers of Stanley--Reisner rings with pure resolutions

The surface of a lattice polytope

The number of permutations with k inversions

Linear equations for the number of intervals which are isomorphic with Boolean lattices and the Dehn--Sommerville equations

The boundary volume of a lattice polytope

$L$ -balancing families

Sets avoiding $p$ -term arithmetic progressions in $Z_{q}^{n}$ are exponentially small

A new upper bound for the size of $s$ -distance sets in boxes

The $f$ --vector of the clique complex of chordal graphs and Betti numbers of edge ideals of uniform hypergraphs