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

[1] AN ALGORITHM TO COMPUTE THE STANLEY DEPTH OF MONOMIAL IDEALS
Rinaldo, Giancarlo
MATEMATICHE, 2008, 63 (02): : 243 - 256
[2] STANLEY DEPTH AND SIZE OF A MONOMIAL IDEAL
Herzog, Juergen
Popescu, Dorin
Vladoiu, Marius
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 140 (02) : 493 - 504
[3] HOW TO COMPUTE THE STANLEY DEPTH OF A MODULE
Ichim, Bogdan
Katthan, Lukas
Jose Moyano-Fernandez, Julio
MATHEMATICS OF COMPUTATION, 2017, 86 (303) : 455 - 472
[4] ON THE STANLEY DEPTH OF MONOMIAL IDEALS
Cimpoeas, Mircea
REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES, 2013, 58 (02): : 205 - 212
[5] Stanley depth of monomial ideals
Popescu, Dorin
BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, 2015, 58 (01): : 95 - 101
[6] Stanley depth of squarefree monomial ideals
Keller, Mitchel T.
Young, Stephen J.
JOURNAL OF ALGEBRA, 2009, 322 (10) : 3789 - 3792
[7] ON THE STANLEY DEPTH AND SIZE OF MONOMIAL IDEALS
Fakhari, S. A. Seyed
GLASGOW MATHEMATICAL JOURNAL, 2017, 59 (03) : 705 - 715
[8] On the Stanley Depth of Powers of Monomial Ideals
Fakhari, S. A. Seyed
MATHEMATICS, 2019, 7 (07)
[9] Stanley depth and Stanley support-regularity of monomial ideals
Yi-Huang Shen
Collectanea Mathematica, 2016, 67 : 227 - 246
[10] Stanley depth and Stanley support-regularity of monomial ideals
Shen, Yi-Huang
COLLECTANEA MATHEMATICA, 2016, 67 (02) : 227 - 246

← 1 2 3 4 5 →