How to compute the Stanley depth of a monomial ideal

被引：102

作者：

Herzog, Huergen ^{[1
]}

Vladoiu, Marius ^{[2
]}

Zheng, Xinxian ^{[1
]}

机构：

[1] Univ Duisburg Essen, Fachbereich Math & Informat, D-45117 Essen, Germany

[2] Univ Bucuresti, Fac Matemat & Informat, RO-010014 Bucharest, Romania

来源：

JOURNAL OF ALGEBRA | 2009年 / 322卷 / 09期

关键词：

Stanley depth; Stanley decomposition; Partitions; Prime filtrations; FILTRATIONS; CONJECTURE; MODULES;

D O I：

10.1016/j.jalgebra.2008.01.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let J subset of I be monomial ideals. We show that the Stanley depth of I/J can be computed in a finite number of steps. We also introduce the fdepth of a monomial ideal which is defined in terms of prime filtrations and show that it can also be computed in a finite number of steps. In both cases it is shown that these invariants can be determined by considering partitions of suitable finite posets into intervals. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：3151 / 3169

页数：19

共 50 条

[31] STANLEY DEPTH OF WEAKLY POLYMATROIDAL IDEALS AND SQUAREFREE MONOMIAL IDEALS
Fakhari, S. A. Seyed
ILLINOIS JOURNAL OF MATHEMATICS, 2013, 57 (03) : 871 - 881
[32] STANLEY DEPTH OF POWERS OF THE EDGE IDEAL OF A FOREST
Pournaki, M. R.
Fakhari, S. A. Seyed
Yassemi, S.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 141 (10) : 3327 - 3336
[33] DEPTH AND STANLEY DEPTH OF POWERS OF THE PATH IDEAL OF A PATH GRAPH
Balanescu, Silviu
Cimpoea, Mircea
UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2024, 86 (04): : 65 - 76
[34] DEPTH AND STANLEY DEPTH OF POWERS OF THE PATH IDEAL OF A PATH GRAPH
Bălănescu, Silviu
Cimpoeaş, Mircea
UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 2024, 86 (04): : 65 - 76
[35] STANLEY DEPTH OF CERTAIN CLASSES OF SQUARE-FREE MONOMIAL IDEALS
Cimpoeas, Mircea
UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2018, 80 (02): : 33 - 40
[36] On the Stanley Depth and the Schmitt-Vogel Number of Squarefree Monomial Ideals
Fakhari, S. A. Seyed
MULTIGRADED ALGEBRA AND APPLICATIONS, 2018, 238 : 77 - 82
[37] STANLEY DEPTH OF THE PATH IDEAL ASSOCIATED TO A LINE GRAPH
Cimpoeas, Mircea
MATHEMATICAL REPORTS, 2017, 19 (02): : 157 - 164
[38] Stanley depth of complete intersection monomial ideals and upper-discrete partitions
Shen, Yi Huang
JOURNAL OF ALGEBRA, 2009, 321 (04) : 1285 - 1292
[39] Depth and Stanley depth of the path ideal associated to an n-cyclic graph
Zhu, Guangjun
TURKISH JOURNAL OF MATHEMATICS, 2017, 41 (05) : 1174 - 1183
[40] Stanley depth of factors of polymatroidal ideals and the edge ideal of forests
A. Alipour
S. A. Seyed Fakhari
S. Yassemi
Archiv der Mathematik, 2015, 105 : 323 - 332

← 1 2 3 4 5 →