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Upper bounds for the size of ordered $L$-intersecting set systems

Gábor Hegedüs

Abstract

A family $\mbox{$\cal F$}=\{F_1,\ldots,F_m\}$ of subsets of $[n]$ is said to be ordered, if there exists an $1\leq r\leq m$ index such that $n\in F_i$ for each $1\leq i\leq r$, $n\notin F_i$ for each $i>r$ and $|F_i|\leq |F_j|$ for each $1\leq i<j\leq m$. Our main result is a new upper bound for the size of ordered $L$-intersecting set systems.

Upper bounds for the size of ordered $L$-intersecting set systems

Abstract

A family \cal F of subsets of is said to be ordered, if there exists an index such that for each , for each and for each . Our main result is a new upper bound for the size of ordered -intersecting set systems.

Paper Structure

This paper contains 2 sections, 4 theorems, 9 equations.

Table of Contents

  1. Introduction
  2. Proof

Key Result

Theorem 1.1

Let $L=\{\ell_1,\ldots ,\ell_s\}$ be a set of $s$ non-negative integers. Let $\hbox{$\cal F$}=\{F_1,\ldots,F_m\}$ be an $L$-intersecting family of subsets of $[n]$. Then

Theorems & Definitions (4)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Proposition 2.1