The MacaulayPosets package for Macaulay2

TL;DR

The paper introduces the MacaulayPosets package for Macaulay2, enabling the study of Macaulay posets, especially those from monomial posets of rings, through specialized data structures and bounds analysis.

Contribution

It provides a new software tool for analyzing Macaulay posets within Macaulay2, leveraging the poset data type for advanced algebraic and combinatorial investigations.

Findings

Enables analysis of Macaulay property in posets

Provides bounds on subset sizes within order ideals

Facilitates study of monomial posets in rings

Abstract

We introduce the package MacaulayPosets written for the computational algebra system Macaulay2. This package utilized the poset data type introduced in the Posets package and offers functionality for studying the Macaulay property for posets, particularly those which arise as monomial posets of commutative rings. A Macaulay poset is characterized by a ranked structure and a total order that interacts harmoniously with the partial order, enabling the establishment of bounds on the sizes of subsets of a given rank within an order ideal.