Polarization of Koszul cycles with applications to powers of edge ideals of whisker graphs

Abstract

In this paper, we introduce the polarization of Koszul cycles and use it to study the depth function of powers of edge ideals of whisker graphs.

Polarization and depolarization of monomial ideals with application to multi-state system reliability

“…One of the main applications is its use to study the Cohen-Macaulay property of monomial ideals by passing to squarefree monomial ideals and applying Reisner's criterion on their associated simplicial complex [28,34]. It is also used to study associated primes of monomial ideals and their powers [20,19,30].…”