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

TL;DR

This paper establishes new upper bounds on the maximum size of ordered $L$-intersecting set systems, which are collections of subsets with a specific ordering and intersection properties.

Contribution

The paper introduces a novel upper bound for the size of ordered $L$-intersecting set systems, advancing understanding of their combinatorial limitations.

Findings

Derived a new upper bound for ordered $L$-intersecting set systems

Improved previous bounds on the size of such set systems

Provides insights into the structure and limitations of ordered intersecting families

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.