Cube-like Incidence Complexes and Their Groups

TL;DR

This paper explores the algebraic structure of automorphism groups of cube-like incidence complexes, focusing on power complexes and generalized power complexes, which resemble higher-dimensional cubes and are relevant in various applications.

Contribution

It provides a detailed analysis of the automorphism groups of power complexes and generalized power complexes, highlighting their cube-like combinatorial properties.

Findings

Automorphism groups exhibit specific algebraic structures.

Power complexes share properties with higher-dimensional cubes.

Applications of power complexes are discussed.

Abstract

The article studies power complexes and generalized power complexes, and investigates the algebraic structure of their automorphism groups. The combinatorial incidence structures involved are cube-like, in the sense that they have many structural properties in common with higher-dimensional cubes and cubical tessellations on manifolds. Power complexes have repeatedly appeared in applications.