Powers of Monomial Ideals and Combinatorics

TL;DR

This paper explores the relationship between powers of monomial ideals in commutative algebra and combinatorial objects like simplicial complexes, polytopes, and graphs, revealing new connections and results.

Contribution

It presents new results on associated primes and depth of monomial ideal powers, linking algebraic properties to combinatorial structures.

Findings

New results on associated primes of monomial ideal powers

Insights into the depth of powers of monomial ideals

Connections between algebraic properties and combinatorial objects

Abstract

This is an exposition of some new results on associated primes and the depth of different kinds of powers of monomial ideals in order to show a deep connection between commutative algebra and some objects in combinatorics such as simplicial complexes, integral points in polytopes and graphs.