Monomial ideals whose depth function has any given number of strict local maxima

TL;DR

This paper demonstrates how to construct monomial ideals with depth functions exhibiting any specified number of strict local maxima, advancing understanding of their algebraic properties.

Contribution

It introduces a method to explicitly construct monomial ideals with depth functions having any desired number of strict local maxima.

Findings

Constructed monomial ideals with arbitrary local maxima in depth functions

Provided explicit examples for each number of maxima

Enhanced understanding of depth function behavior in monomial ideals

Abstract

We construct monomial ideals with the property that their depth function has any given number of strict local maxima.