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2010

Matroid Polytopes and their Volumes

9 years 6 days ago
Matroid Polytopes and their Volumes
We express the matroid polytope PM of a matroid M as a signed Minkowski sum of simplices, and obtain a formula for the volume of PM . This gives a combinatorial expression for the degree of an arbitrary torus orbit closure in the Grassmannian Grk,n. We then derive analogous results for the independent set polytope and the associated flag matroid polytope of M. Our proofs are based on a natural extension of Postnikov's theory of generalized permutohedra.
Federico Ardila, Carolina Benedetti, Jeffrey Doker
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2010
Where DCG
Authors Federico Ardila, Carolina Benedetti, Jeffrey Doker
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