A note on almost Cohen-Macaulay monomial ideals

TL;DR

This paper investigates the properties of almost Cohen-Macaulay monomial ideals, providing characterizations for specific classes like polymatroidal Veronese type and transversal polymatroidal ideals, with illustrative examples.

Contribution

It offers new characterizations of almost Cohen-Macaulay monomial ideals, especially for polymatroidal classes, expanding understanding of their algebraic and combinatorial structure.

Findings

Characterization of almost Cohen-Macaulay polymatroidal Veronese type ideals

Characterization of almost Cohen-Macaulay transversal polymatroidal ideals

Examples illustrating the concepts and classifications

Abstract

Let $R = k[x_1,\ldots, x_n]$ be the polynomial ring in $n$ variables over a field $k$ and let $I$ be a monomial ideal of $R$. In this paper, we study almost Cohen-Macaulay simplicial complex. Moreover, we characterize the almost Cohen-Macaulay polymatroidal Veronese type and transversal polymatroidal ideals and furthermore we give some examples.