Application of hypergraph Hoffman's bound to intersecting families

TL;DR

This paper applies hypergraph Hoffman's bound via the Filmus-Golubev-Lifshitz method to analyze intersecting families, providing new bounds and stability results for measure versions of classical combinatorial theorems.

Contribution

It introduces a novel application of Hoffman's bound to hypergraphs for intersecting families, extending stability results in measure versions of Erdős-Ko-Rado.

Findings

Bound the independence number of hypergraphs using the method.

Prove a stability result for measure versions of Erdős-Ko-Rado.

Address problems on multiply intersecting families with biased measure.

Abstract

Using the Filmus-Golubev-Lifshitz method to bound the independence number of a hypergraph, we solve some problems concerning multiply intersecting families with biased measure. Among other results we obtain a stability result of a measure version of the Erdos-Ko-Rado theorem for multiply intersecting families.