Pure O-Sequences and Matroid h-Vectors
Author(s)Ha, Huy Tai; Stokes, Erik; Zanello, Fabrizio
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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. At the end of the paper, using our method, we discuss a first possible approach to Stanley’s conjecture in full generality. Our technical work on pure O-sequences also uses very recent results of the third author and collaborators.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Annals of Combinatorics
Ha, Huy Tai, Erik Stokes, and Fabrizio Zanello. “Pure O-Sequences and Matroid h-Vectors.” Ann. Comb. 17, no. 3 (September 2013): 495–508.
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