Geodesic
\(h\)-vectors of small matroid complexes
The electronic journal of combinatorics, Tome 19 (2012) no. 1
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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.
DOI : 10.37236/1165
Classification : 05E45, 05B35
Mots-clés : \(h\)-vector of a matroid simplicial complex 
@article{10_37236_1165,
     author = {Jes\'us A. De Loera and Yvonne Kemper and Steven Klee},
     title = {\(h\)-vectors of small matroid complexes},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {1},
     doi = {10.37236/1165},
     zbl = {1244.05238},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1165/}
}
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Jesús A. De Loera; Yvonne Kemper; Steven Klee. \(h\)-vectors of small matroid complexes. The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/1165

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