Geodesic
Internally perfect matroids
The electronic journal of combinatorics, Tome 24 (2017) no. 2
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In 1977 Stanley proved that the $h$-vector of a matroid is an $\mathcal{O}$-sequence and conjectured that it is a pure $\mathcal{O}$-sequence. In the subsequent years the validity of this conjecture has been shown for a variety of classes of matroids, though the general case is still open. In this paper we use Las Vergnas' internal order to introduce a new class of matroids which we call internally perfect. We prove that these matroids satisfy Stanley's Conjecture and compare them to other classes of matroids for which the conjecture is known to hold. We also prove that, up to a certain restriction on deletions, every minor of an internally perfect ordered matroid is internally perfect.
DOI : 10.37236/5746
Classification : 05B35, 52B40
Mots-clés : Stanley's conjecture, \(h\)-vector, matroid, internal order, internally perfect basis, internally perfect matroid 
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     author = {Aaron Dall},
     title = {Internally perfect matroids},
     journal = {The electronic journal of combinatorics},
     year = {2017},
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     number = {2},
     doi = {10.37236/5746},
     zbl = {1366.05023},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/5746/}
}
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Aaron Dall. Internally perfect matroids. The electronic journal of combinatorics, Tome 24 (2017) no. 2. doi: 10.37236/5746

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