## Splittings of monomial ideals

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- by Christopher A. Francisco, Huy Tài Hà and Adam Van Tuyl PDF
- Proc. Amer. Math. Soc.
**137**(2009), 3271-3282 Request permission

## 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.## References

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## Additional Information

**Christopher A. Francisco**- Affiliation: Department of Mathematics, Oklahoma State University, 401 Mathematical Sciences, Stillwater, Oklahoma 74078
- MR Author ID: 719806
- Email: chris@math.okstate.edu
**Huy Tài Hà**- Affiliation: Department of Mathematics, Tulane University, 6823 St. Charles Avenue, New Orleans, Louisiana 70118
- ORCID: 0000-0002-6002-3453
- Email: tai@math.tulane.edu
**Adam Van Tuyl**- Affiliation: Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario P7B 5E1, Canada
- MR Author ID: 649491
- ORCID: 0000-0002-6799-6653
- Email: avantuyl@lakeheadu.ca
- 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
- © Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**137**(2009), 3271-3282 - MSC (2000): Primary 13D02, 13P10, 13F55, 05C99
- DOI: https://doi.org/10.1090/S0002-9939-09-09929-8
- MathSciNet review: 2515396