Depth and Stanley depth of powers of the edge ideals of some caterpillar and lobster trees

2022/02/26 by Tooba Zahid, Zahid, Tooba, Zunaira Sajid +3
Computer Science · Mathematics · #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.2202.13183

openalex publication_date 2022/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be a ring of polynomials in finitely many variables over a field. In this paper we give lower bounds for depth and Stanley depth of modules of the type S/I^t for t≥1, where I is the edge ideal of some caterpillar and lobster trees. These new bounds are much sharper than the existing bounds for the classes of ideals we considered.

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