Pure O-sequences and matroid h-vectors

Details Pure O-sequences and matroid h-vectors Pure O-sequences and matroid h-vectors

2010-06-02

arxiv.org/abs/1006.0325v1

Mathematics

Combinatorics

13 pages

Scientific paper

We study Stanley's long-standing conjecture that the h-vectors of matroid simplicial complexes are pure O-sequences. Our method consists of a new and more abstract approach, which shifts the focus from working on constructing suitable artinian level monomial ideals, as often done in the past, to the study of properties of pure O-sequences. We propose a conjecture on pure O-sequences and settle it in small socle degrees. This allows us to prove Stanley's conjecture for all matroids of rank 3. Our technical work on pure O-sequences also uses very recent results of the third author in collaboration with Boij, Migliore, Mir\`o-Roig and Nagel.

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