Fractional L-intersecting families

Abstract

Let $L=\{\frac{a_1}{b_1},\dots ,\frac{a_s}{b_s}\}$, where for every $i\in [s]$, $\frac{a_i}{b_i}\in [0,1)$ is an irreducible fraction. Let $\mathcal{F}=\{A_1,\dots ,A_m\}$ be a family of subsets of $[n]$. We say $\mathcal{F}$ is a \emph{fractional $L$-intersecting family} if for every distinct $i,j\in [m]$, there exists an $\frac{a}{b}\in L$ such that $|A_i\cap A_j|\in \{\frac{a}{b}|A_i|,\frac{a}{b}|A_j|\}$. In this paper, we introduce and study the notion of fractional $L$-intersecting families.

10 pages