×

zbMATH — the first resource for mathematics

Generalized permutohedra, \(h\)-vectors of cotransversal matroids and pure \(O\)-sequences. (English) Zbl 1295.52017
Summary: Stanley has conjectured that the \(h\)-vector of a matroid complex is a pure \(O\)-sequence. We will prove this for cotransversal matroids by using generalized permutohedra. We construct a bijection between lattice points inside an \(r\)-dimensional convex polytope and bases of a rank \(r\) transversal matroid.

MSC:
52B40 Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)
05A19 Combinatorial identities, bijective combinatorics
PDF BibTeX XML Cite
Full Text: Link arXiv