Lexsegment ideals of Hilbert depth 1

Yi-Huang Shen

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arXiv · 1208.1822

Lexsegment ideals of Hilbert depth 1

Yi-Huang Shen

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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.

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Yi-Huang Shen. 2012-08-09. Lexsegment ideals of Hilbert depth 1. https://arxiv.org/abs/1208.1822

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