Betti numbers and almost complete intersection monomial ideals

TL;DR

This paper provides explicit formulas for Betti numbers of almost complete intersection monomial ideals, facilitating their minimal free resolutions, and characterizes their Cohen-Macaulayness.

Contribution

It introduces a new explicit formula for Betti numbers of almost complete intersection monomial ideals and characterizes their Cohen-Macaulayness.

Findings

Explicit Betti number formulas for these ideals

Characterization of Cohen-Macaulayness

Extension to dominant monomial ideals

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 present an explicit formula for the Betti numbers of almost complete intersection monomial ideals, which enables a rapid construction of their minimal free resolutions. In addition, we characterize the Cohen-Macaulayness of these ideals and also we show the same result for dominant monomial ideals.