The h-vectors of 1-dimensional Matroid Complexes and a Conjecture of Stanley

2009/03/20 by Stokes, Erik
#13F55 (Primary) 05B35 (Secondary) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.0903.3569

Abstract

A matroid complex is a pure complex such that every restriction is again pure. It is a long-standing open problem to classify all possible h-vectors of such complexes. In the case when the complex has dimension 1 we completely resolve this question. We also prove the 1-dimensional case of a conjecture of Stanley that all matroid h-vectors are pure O-sequences. Finally, we completely characterize the Stanley-Reisner ideals of 1-dimensional matroid complexes.

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