## 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.## References

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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