On the Hilbert depth of certain monomial ideals and applications

2023/06/19 by Silviu Bălănescu, Balanescu, Silviu, Mircea Cimpoeaş +1
Computer Science · Mathematics · #05A18 #06A07 #13C15 #13F20 #13P10 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2306.11015

openalex publication_date 2023/06/19 · openalex created_date 2023/06/22 · openalex updated_date 2026/07/28

Abstract

We study the Stanley depth and the Hilbert depth for I and S/I, where I⊂ S=K[x₁,…,x_N] is the intersection of monomial prime ideals with disjoint sets of variables. As an application, we obtain bounds for the Stanley depth of I_n,m^t and J_n,m^t, where I_n,m is the m-path ideal of the path graph of length n and J_n,m is the the m-path ideal of the cycle graph of length n.

Related

• Values and bounds of the Stanley depth
• How to compute the Stanley depth of a monomial ideal
• Remarks on the Stanley depth and Hilbert depth of monomial ideals with linear quotients
• On the Hilbert depth of monomial ideals
• Upper bounds for the Stanley depth