Generalized permutohedra, \(h\)-vectors of cotransversal matroids and pure \(O\)-sequences. (English) Zbl 1295.52017

Oh, Suho

Electron. J. Comb. 20, No. 3, Research Paper P14, 14 p. (2013).

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

Keywords:

matroids; polytopes; \(h\)-vector; bipartite graphs