Shellable flag simplicial complexes of non-simple polyominoes

TL;DR

This paper explores the shellability of flag simplicial complexes associated with non-simple, thin polyominoes, revealing their Cohen-Macaulay properties and providing a combinatorial interpretation of their $h$-polynomial.

Contribution

It introduces new results on the shellability and Cohen-Macaulayness of complexes linked to non-simple polyominoes, with a novel combinatorial interpretation of their $h$-polynomial.

Findings

Shellability of flag simplicial complexes for non-simple polyominoes established.

Cohen-Macaulayness of the related coordinate rings proven.

Combinatorial interpretation of the $h$-polynomial provided.

Abstract

In this article we investigate the shellability of the flag simplicial complexes attached to non-simple and thin polyominoes. As a consequence, we obtain the Cohen-Macaulayness and a combinatorial interepetation of the $h$-polynomial of the related coordinate rings.