Splittings of monomial ideals

Francisco, Christopher; Hà, Huy; Van Tuyl, Adam

doi:10.1090/S0002-9939-09-09929-8

Splittings of monomial ideals
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by Christopher A. Francisco, Huy Tài Hà and Adam Van Tuyl

Proc. Amer. Math. Soc. 137 (2009), 3271-3282

DOI: https://doi.org/10.1090/S0002-9939-09-09929-8

Published electronically: 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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