Lexsegment ideals of Hilbert depth 1

2012/08/09 by Shen, Yi-Huang
#05C70 (Secondary) #05E40 #05E45 #06A07 (Primary) 13C13 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1208.1822

Abstract

Let I⊂ S=\KK[x₁,...,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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