A Macaulay2 Package for Stanley Simplicial Poset Ideals

TL;DR

This paper introduces a Macaulay2 package named SimplicialPosets for working with simplicial posets and their Stanley-Reisner ideals, along with a new random model for simplicial posets that extends existing models for random complexes.

Contribution

The paper presents a new Macaulay2 package for simplicial posets and a novel random model generalizing existing models for random simplicial complexes.

Findings

Implementation of the SimplicialPosets package in Macaulay2

Introduction of a new random model for simplicial posets

Extension of the Kahle model for random simplicial complexes

Abstract

We give a description of a new Macaulay2 package called SimplicialPosets. This package provides functions for working with simplicial posets and calculating their generalized Stanley-Reisner ideals. For practical purposes, we also introduce of a new random model for a class of simplicial posets which generalizes existing models for random simplicial complexes such as the Kahle model.