$h$-vectors of small matroid complexes

Details $h$-vectors of small matroid complexes $h$-vectors of small matroid complexes

2011-06-13

arxiv.org/abs/1106.2576v1

Mathematics

Combinatorics

11 pages, 1 figure

Scientific paper

Stanley conjectured in 1977 that the $h$-vector of a matroid simplicial
complex is a pure $O$-sequence. We give simple constructive proofs that the
conjecture is true for matroids of rank less than or equal to 3, and corank 2.
We used computers to verify that Stanley's conjecture holds for all matroids on
at most nine elements.

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