Lexsegment ideals of Hilbert depth 1

Abstract

Let $I\subset S=\KK[x_1,...,x_n]$ be a lexsegment ideal, generated by monomials of degree $d$. The main aim of this paper is to characterize when the Hilbert depth of $I$ will be 1, in the standard graded case. In addition to this, we will give an estimate of depth of squarefree monomial ideals, generalizing a result of Popescu. We will also show that Stanley conjecture holds for squarefree stable ideals, in the multigraded case.

14 pages

References in corpus (6)

• An inequality between depth and Stanley depth
• Stanley depth of square free Veronese ideals
• The Stanley conjecture on monomial almost complete intersection ideals
• Lexsegment ideals are sequentially Cohen-Macaulay
• On a conjecture of Stanley depth of squarefree Veronese ideals
• On Two Classes of Closely Related Monomial Ideals

Cited by in corpus (8)

• Depth of some square free monomial ideals
• Depth of some special monomial ideals
• Three generated, squarefree, monomial ideals
• Stanley depth on five generated, squarefree, monomial ideals
• How to compute the Hilbert depth of a graded ideal
• An algorithm to compute the Hilbert depth
• Depth in a pathological case
• Stanley depth of monomial ideals