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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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Bounding the projective dimension of a squarefree monomial ideal via domination in clutters
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by Hailong Dao and Jay Schweig PDF
Proc. Amer. Math. Soc. 143 (2015), 555-565 Request permission

Abstract:

We introduce the concept of edgewise domination in clutters and use it to provide an upper bound for the projective dimension of any squarefree monomial ideal. We then compare this bound to a bound given by Faltings. Finally, we study a family of clutters associated to graphs and compute domination parameters for certain classes of these clutters.
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Additional Information
  • Hailong Dao
  • Affiliation: Department of Mathematics, University of Kansas, 1460 Jayhawk, Lawrence, Kansas 66045
  • MR Author ID: 828268
  • Jay Schweig
  • Affiliation: Department of Mathematics, 401 MSCS, Oklahoma State University, Stillwater, Oklahoma 74075
  • MR Author ID: 702558
  • Received by editor(s): February 17, 2013
  • Received by editor(s) in revised form: March 27, 2013, and May 29, 2013
  • Published electronically: October 10, 2014
  • Additional Notes: The first author was partially supported by NSF grants DMS 0834050 and DMS 1104017
  • Communicated by: Irena Peeva
  • © Copyright 2014 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 555-565
  • MSC (2010): Primary 05C10, 05C65, 05C69, 13D02, 05E45
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12374-4
  • MathSciNet review: 3283644