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Bounding the projective dimension of a squarefree monomial ideal via domination in clutters


Authors: Hailong Dao and Jay Schweig
Journal: Proc. Amer. Math. Soc. 143 (2015), 555-565
MSC (2010): Primary 05C10, 05C65, 05C69, 13D02, 05E45
DOI: https://doi.org/10.1090/S0002-9939-2014-12374-4
Published electronically: October 10, 2014
MathSciNet review: 3283644
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Abstract: We introduce the concept of edgewise domination in clutters and use it to provide an upper bound for the projective dimension of any squarefree monomial ideal. We then compare this bound to a bound given by Faltings. Finally, we study a family of clutters associated to graphs and compute domination parameters for certain classes of these clutters.


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Additional Information

Hailong Dao
Affiliation: Department of Mathematics, University of Kansas, 1460 Jayhawk, Lawrence, Kansas 66045
MR Author ID: 828268

Jay Schweig
Affiliation: Department of Mathematics, 401 MSCS, Oklahoma State University, Stillwater, Oklahoma 74075
MR Author ID: 702558

Received by editor(s): February 17, 2013
Received by editor(s) in revised form: March 27, 2013, and May 29, 2013
Published electronically: October 10, 2014
Additional Notes: The first author was partially supported by NSF grants DMS 0834050 and DMS 1104017
Communicated by: Irena Peeva
Article copyright: © Copyright 2014 American Mathematical Society