Inverse Expander Mixing for Hypergraphs

TL;DR

This paper develops inverse mixing lemmas for hypergraphs and simplicial complexes, extending graph results and addressing open questions in higher-dimensional combinatorial structures.

Contribution

It introduces inverse mixing lemmas for hypergraphs and simplicial complexes, generalizing known graph results and solving an open problem in the field.

Findings

Established inverse mixing lemmas for hypergraphs

Extended Bilu-Linial results to hypergraph settings

Answered a key open question in simplicial complexes

Abstract

We formulate and prove inverse mixing lemmas in the settings of simplicial complexes and k-uniform hypergraphs. In the hypergraph setting, we extend results of Bilu and Linial for graphs. In the simplicial complex setting, our results answer a question of Parzanchevski et al.