Splittings of monomial ideals
Authors:
Christopher A. Francisco, Huy Tài Hà and Adam Van Tuyl
Journal:
Proc. Amer. Math. Soc. 137 (2009), 32713282
MSC (2000):
Primary 13D02, 13P10, 13F55, 05C99
Published electronically:
May 7, 2009
MathSciNet review:
2515396
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
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 CohenMacaulay 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 characteristicdependent.
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 S. Eliahou and M. Kervaire, Minimal resolutions of some monomial ideals. J. Algebra 129 (1990), no. 1, 125. MR 1037391 (91b:13019)
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 G. Fatabbi, On the resolution of ideals of fat points. J. Algebra 242 (2001), no. 1, 92108. MR 1844699 (2002d:13015)
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 C. A. Francisco, Resolutions of small sets of fat points. J. Pure Appl. Algebra 203 (2005), no. 13, 220236. MR 2176661 (2006f:13012)
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 C.A. Francisco and A. Van Tuyl, Sequentially CohenMacaulay edge ideals. Proc. Amer. Math. Soc. 135 (2007), no. 8, 23272337. MR 2302553 (2008a:13030)
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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/S0002993909099298
PII:
S 00029939(09)099298
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.
