The structure of the Boij-Söderberg posets

Details The structure of the Boij-Söderberg posets The structure of the Boij-Söderberg posets

2010-06-10

arxiv.org/abs/1006.2026v1

Proceedings of the American Mathematical Society 139 (2011), no. 6, 2009-2015

Mathematics

Combinatorics

7 pages, 2 figures

Scientific paper

Boij and S\"oderberg made a pair of conjectures, which were subsequently proven by Eisenbud and Schreyer and then extended by Boij and S\"oderberg, about 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 the posets are bounded complete lattices and the order complexes are vertex-decomposable, hence Cohen-Macaulay and squarefree glicci.

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