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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Stanley depth and size of a monomial ideal
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by Jürgen Herzog, Dorin Popescu and Marius Vladoiu PDF
Proc. Amer. Math. Soc. 140 (2012), 493-504 Request permission

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
  • MR Author ID: 189999
  • 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
  • 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
  • © Copyright 2011 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 493-504
  • MSC (2010): Primary 13C15; Secondary 13P10, 13F55, 13F20
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11160-2
  • MathSciNet review: 2846317