Betti numbers of mixed product ideals

TL;DR

This paper calculates the Betti numbers for a specific class of square-free monomial ideals called mixed product ideals, and determines their type when they are Cohen-Macaulay, advancing understanding of their algebraic properties.

Contribution

It provides explicit Betti number calculations for mixed product ideals and characterizes their Cohen-Macaulay type, a novel contribution to algebraic combinatorics.

Findings

Betti numbers of mixed product ideals are explicitly computed.

Cohen-Macaulay mixed product ideals have their type determined.

The results deepen understanding of the algebraic structure of these ideals.

Abstract

We compute the Betti numbers of the resolution of a special class of square-free monomial ideals, the ideals of mixed products. Moreover when these ideals are Cohen-Macaulay we calculate their type.