SimplicialDecomposability: a package for Macaulay 2

TL;DR

The paper introduces the SimplicialDecomposability package for Macaulay 2, enabling computation of shelling orders and decomposability properties of simplicial complexes, enhancing computational tools in algebraic topology.

Contribution

It provides new methods for computing shelling orders and decomposability properties within Macaulay 2, extending existing capabilities for simplicial complex analysis.

Findings

Successfully computes shelling orders for simplicial complexes.

Implements methods for vertex- and k-decomposability detection.

Enhances computational tools for algebraic topology in Macaulay 2.

Abstract

We introduce a new Macaulay 2 package, SimplicialDecomposability, which works in conjunction with the extant package SimplicialComplexes in order to compute a shelling order, if one exists, of a specified simplicial complex. Further, methods for determining vertex-decomposability are implemented, along with methods for determining k-decomposability.