Ideals with linear quotients and componentwise polymatroidal ideals

2021/08/01 by Somayeh Bandari, Bandari, Somayeh, Ayesha Asloob Qureshı +1
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.2108.00531

openalex publication_date 2021/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If I is a monomial ideal with linear quotients, then it has componentwise linear quotients. However, the converse of this statement is an open question. In this paper, we provide two classes of ideals for which the converse of this statement holds. First class is the componentwise polymatroidal ideals in K[x,y] and the second one is the componentwise polymatroidal ideals with strong exchange property.

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