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Algorithms for strongly stable ideals


Authors: Dennis Moore and Uwe Nagel
Journal: Math. Comp. 83 (2014), 2527-2552
MSC (2010): Primary 14Q20, 13P99
DOI: https://doi.org/10.1090/S0025-5718-2014-02784-1
Published electronically: January 6, 2014
MathSciNet review: 3223345
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Abstract: Strongly stable monomial ideals are important in algebraic geometry, commutative algebra, and combinatorics. Prompted, for example, by combinatorial approaches for studying Hilbert schemes and the existence of maximal total Betti numbers among saturated ideals with a given Hilbert polynomial, in this paper we present three algorithms to produce all strongly stable ideals with certain prescribed properties: the saturated strongly stable ideals with a given Hilbert polynomial, the almost lexsegment ideals with a given Hilbert polynomial, and the saturated strongly stable ideals with a given Hilbert function. We also establish results for estimating the complexity of our algorithms.


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Additional Information

Dennis Moore
Affiliation: Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, Kentucky 40506-0027
Email: dennikm@gmail.com

Uwe Nagel
Affiliation: Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, Kentucky 40506-0027
Email: uwe.nagel@uky.edu

DOI: https://doi.org/10.1090/S0025-5718-2014-02784-1
Keywords: Hilbert polynomial, strongly stable ideal, Betti numbers, Castelnuovo-Mumford regularity, lexsegment ideal
Received by editor(s): October 12, 2011
Received by editor(s) in revised form: January 9, 2013
Published electronically: January 6, 2014
Additional Notes: This work was partially supported by a grant from the Simons Foundation (#208869 to Uwe Nagel).
The authors were also partially supported by the National Security Agency under Grant Number H98230-09-1-0032.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.