# 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
##### Keywords:
matroids; polytopes; $$h$$-vector; bipartite graphs
Full Text: