G. Hegedus

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20102021

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6 papers · 1 filter

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.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.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…

Non-uniform skew versions of Bollobás' Theorem

An uniform version of Dvir and Moran's theorem

L-balancing families

A new proof of a generalization of Gerzon's bound

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

A note on linear Sperner families

$L$ -balancing families

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