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 | References | Similar Articles | 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 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:
https://doi.org/10.1090/S0002-9939-09-09929-8

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.