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

Dao, Hailong; Schweig, Jay

doi:10.1090/S0002-9939-2014-12374-4

Bounding the projective dimension of a squarefree monomial ideal via domination in clutters
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by Hailong Dao and Jay Schweig PDF

Proc. Amer. Math. Soc. 143 (2015), 555-565 Request permission

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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