Polarization and spreading of monomial ideals

Abstract

We characterize the monomial ideals $I\subset K[x_1,\dots ,x_n]$ with the property that the polarization $I^p$ and $I^{{\sigma }^n}:=$ the ideal obtained from $I$ by the $n$-th iterated squarefree operator $\sigma$ are isomorphic via a permutation of variables. We give several methods to construct such ideals. We also compare the depth and sdepth of $I$ and $I^{{\sigma }^n}$.

19 pages

References in corpus (3)

• Stanley depth and the lcm-lattice
• t-spread strongly stable monomial ideals
• A class of square-free monomial ideals associated to two integer sequences