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

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

2009-03-20

arxiv.org/abs/0903.3569v1

Mathematics

Commutative Algebra

24 pages with 2 figures. submitted to J. Algebraic Comb

Scientific paper

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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