Polarization and depolarization of monomial ideals with application to multistate system reliability

TL;DR

This paper explores the depolarizations of squarefree monomial ideals, providing a method to find all depolarizations and applying these concepts to analyze multistate system reliability.

Contribution

It introduces a systematic approach to identify all depolarizations of a monomial ideal and applies polarization techniques to multistate system reliability analysis.

Findings

Method to find all depolarizations of a monomial ideal

Shared properties among depolarizations identified

Application to multistate system reliability analysis

Abstract

We study the family of depolarizations of a squarefree monomial ideal $I$, i.e. all monomial ideals whose polarization is $I$. We describe a method to find all depolarizations of $I$ and study some of the properties they share and some they do not share. We then apply polarization and depolarization tools to study the reliability of multi-state coherent systems via binary systems and vice versa.