Stanley depth and size of a monomial ideal

Authors:
Jürgen Herzog, Dorin Popescu and Marius Vladoiu

Journal:
Proc. Amer. Math. Soc. **140** (2012), 493-504

MSC (2010):
Primary 13C15; Secondary 13P10, 13F55, 13F20

Published electronically:
July 5, 2011

MathSciNet review:
2846317

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Abstract | References | Similar Articles | Additional Information

Abstract: Lyubeznik introduced the concept of size of a monomial ideal and showed that the size of a monomial ideal increased by is a lower bound for its depth. We show that the size increased by is also a lower bound for its Stanley depth. Applying Alexander duality we obtain upper bounds for the regularity and Stanley regularity of squarefree monomial ideals.

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Additional Information

**Jürgen Herzog**

Affiliation:
Fachbereich Mathematik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany

Email:
juergen.herzog@uni-essen.de

**Dorin Popescu**

Affiliation:
Institute of Mathematics “Simion Stoilow” of the Romanian Academy, University of Bucharest, P. O. Box 1-764, Bucharest 014700, Romania

Email:
dorin.popescu@imar.ro

**Marius Vladoiu**

Affiliation:
Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, Bucharest, RO-010014, Romania

Email:
vladoiu@gta.math.unibuc.ro

DOI:
https://doi.org/10.1090/S0002-9939-2011-11160-2

Received by editor(s):
November 30, 2010

Published electronically:
July 5, 2011

Additional Notes:
This paper was partially written during the visit of the first author at the Institute of Mathematics “Simion Stoilow” of the Romanian Academy supported by a BitDefender Invited Professor Scholarship, 2010

The second and third authors were partially supported by the CNCSIS grant PN II-542/2009, respectively CNCSIS grant TE$_46$ no. 83/2010, of the Romanian Ministry of Education, Research and Innovation. They also want to express their gratitude to ASSMS of GC University Lahore for creating a very appropriate atmosphere for research work.

Communicated by:
Irena Peeva

Article copyright:
© Copyright 2011
American Mathematical Society