Higher dimensional Moore bounds

TL;DR

This paper extends the Moore bound concept from graph theory to higher-dimensional simplicial complexes, providing upper bounds on their face numbers based on a generalized girth measure.

Contribution

It introduces a generalized girth for simplicial complexes and establishes upper bounds on face numbers, bridging graph theory and higher-dimensional topology.

Findings

Derived upper bounds on face numbers using generalized girth

Extended Moore bound concepts to simplicial complexes

Provided a new framework linking girth and face enumeration

Abstract

We prove upper bounds on the face numbers of simplicial complexes in terms on their girths, in analogy with the Moore bound from graph theory. Our definition of girth generalizes the usual definition for graphs.