Decomposition Complexes

TL;DR

This paper introduces decomposition complexes of posets, a new mathematical structure that generalizes order complexes and remains closed under products, unifying various existing complexes like nested set and Bergman complexes.

Contribution

The paper presents the concept of decomposition complexes of posets, expanding the theory of order complexes and unifying several important classes of complexes.

Findings

Decomposition complexes generalize order complexes.

They are closed under taking products.

Include nested set and Bergman complexes as special cases.

Abstract

We introduce decomposition complexes of posets, which generalize order complexes. The main advantage of our construction is that decomposition complexes are closed under taking products. Other special instances of this theory include nested set complexes as well as Bergman complexes.