Stanley depth of squarefree monomial ideals

JOURNAL OF ALGEBRA

卷:322

Article

Keller, Mitchel T.¹  Young, Stephen J.¹ 

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

关键词: Stanley depth;    Squarefree monomial ideal;    Boolean lattice;    Partition;    Interval;   

DOI  :  10.1016/j.jalgebra.2009.05.021

来源: Elsevier

【 摘 要 】

In this paper, we answer a question posed by Y.H. Shen. We prove that if I is an m-generated squarefree monomial ideal in the polynomial ring S = K[x(1), ..., x(n)] with K a field, then sclepth I >= n - left perpendicularm/2right perpendicular. The proof is inductive and uses the correspondence between a Stanley decomposition of a monomial ideal and a partition of a particular poset into intervals established by Herzog, Vladoiu and Zheng. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free