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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Splittings of monomial ideals


Authors: Christopher A. Francisco, Huy Tài Hà and Adam Van Tuyl
Journal: Proc. Amer. Math. Soc. 137 (2009), 3271-3282
MSC (2000): Primary 13D02, 13P10, 13F55, 05C99
Published electronically: May 7, 2009
MathSciNet review: 2515396
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Abstract: We provide some new conditions under which the graded Betti numbers of a monomial ideal can be computed in terms of the graded Betti numbers of smaller ideals, thus complementing Eliahou and Kervaire's splitting approach. As applications, we show that edge ideals of graphs are splittable, and we provide an iterative method for computing the Betti numbers of the cover ideals of Cohen-Macaulay bipartite graphs. Finally, we consider the frequency with which one can find particular splittings of monomial ideals and raise questions about ideals whose resolutions are characteristic-dependent.


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Additional Information

Christopher A. Francisco
Affiliation: Department of Mathematics, Oklahoma State University, 401 Mathematical Sciences, Stillwater, Oklahoma 74078
Email: chris@math.okstate.edu

Huy Tài Hà
Affiliation: Department of Mathematics, Tulane University, 6823 St. Charles Avenue, New Orleans, Louisiana 70118
Email: tai@math.tulane.edu

Adam Van Tuyl
Affiliation: Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario P7B 5E1, Canada
Email: avantuyl@lakeheadu.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09929-8
PII: S 0002-9939(09)09929-8
Received by editor(s): July 14, 2008
Received by editor(s) in revised form: February 13, 2009
Published electronically: May 7, 2009
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.