The structure of the Boij-Söderberg posets

Cook, David, II

doi:10.1090/S0002-9939-2010-10791-8

The structure of the Boij-Söderberg posets
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Proc. Amer. Math. Soc. 139 (2011), 2009-2015 Request permission

Abstract:

Boij and Söderberg made a pair of conjectures, which were subsequently proven by Eisenbud and Schreyer and then extended by Boij and Söderberg, concerning the structure of Betti diagrams of graded modules. In the theory, a particular family of posets and their associated order complexes play an integral role. We explore the structure of this family. In particular, we show that the posets are bounded complete lattices and the order complexes are vertex-decomposable, hence Cohen-Macaulay and squarefree glicci.

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