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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: Lyubeznik introduced the concept of size of a monomial ideal and showed that the size of a monomial ideal increased by $ 1$ is a lower bound for its depth. We show that the size increased by $ 1$ 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: http://dx.doi.org/10.1090/S0002-9939-2011-11160-2
PII: S 0002-9939(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