The behavior of Stanley depth under polarization

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:135

Article

Ichim, B.¹  Katthaen, L.²  Moyano-Fernandez, J. J.^3,4 

[1] Romanian Acad, Simion Stoilow Inst Math, Bucharest 014700, Romania

[2] Univ Osnabruck, Fachbereich Math Informat, D-49069 Osnabruck, Germany

[3] Univ Jaume 1, Dept Matemat, Castellon De La Plana 12071, Spain

[4] Univ Jaume 1, IMAC Inst Univ Matemat & Aplicac Castello, Castellon De La Plana 12071, Spain

关键词: Monomial ideal;    Stanley depth;    Stanley decomposition;    Poset map;    Polarization;   

DOI  :  10.1016/j.jcta.2015.05.005

来源: Elsevier

【 摘 要 】

Let K be a field, R = K[X-1, ... , X-n] be the polynomial ring and J subset of I be two monomial ideals in R. In this paper we show that sdepth I/J - depth I/J = sdepth I-p/J(p) - depth I-p/J(p), where sdepth I/J denotes the Stanley depth and I-p denotes Polarization the polarization. This solves a conjecture by Herzog [9] and reduces the famous Stanley conjecture (for modules of the form I/J) to the squarefree case. As a consequence, the Stanley conjecture for algebras of the form Rh I and the well-known combinatorial conjecture that every Cohen-Macaulay simplicial complex is partitionable are equivalent. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free