Proceedings of the American Mathematical Society

Author(s): Christopher A. Francisco; Huy Tài Hà; Adam Van Tuyl
Journal: Proc. Amer. Math. Soc. 137 (2009), 3271-3282.
MSC (2000): Primary 13D02, 13P10, 13F55, 05C99
Posted: May 7, 2009
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 13D02, 13P10, 13F55, 05C99

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

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