Lucas sequences in t-uniform simplicial complexes

TL;DR

This paper introduces t-uniform simplicial complexes and demonstrates that the sphere lengths in these complexes follow Lucas sequences, also establishing optimal constants for the linear isoperimetric inequality in hyperbolic cases.

Contribution

The paper defines t-uniform simplicial complexes and links sphere lengths to Lucas sequences, providing new insights into their geometric properties and isoperimetric inequalities.

Findings

Sphere lengths in t-uniform complexes follow Lucas sequences

Optimal constants for linear isoperimetric inequality in hyperbolic complexes

Introduction of t-uniform simplicial complexes

Abstract

We introduce t-uniform simplicial complexes and we show that the lengths of spheres in such complexes are the terms of certain Lucas sequences. We find optimal constants for the linear isoperimetric inequality in the hyperbolic case.