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Mathematics of Computation

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

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Algorithms for strongly stable ideals
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by Dennis Moore and Uwe Nagel PDF
Math. Comp. 83 (2014), 2527-2552 Request permission

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
  • MR Author ID: 248652
  • Email: uwe.nagel@uky.edu
  • 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.
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 2527-2552
  • MSC (2010): Primary 14Q20, 13P99
  • DOI: https://doi.org/10.1090/S0025-5718-2014-02784-1
  • MathSciNet review: 3223345