The MacaulayPosets package for Macaulay2

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.