Abstract We express the matroid polytope P
M
of a matroid M as a signed Minkowski sum of simplices, and obtain a formula for the volume of P
M
. This gives a combinatorial expression for the degree of an arbitrary torus orbit closure in the Grassmannian Gr
k,n
. We then derive analogous results for the independent set polytope and the underlying flag matroid polytope of M. Our proofs are based on a natural extension of Postnikov’s theory of generalized permutohedra.
M
of a matroid M as a signed Minkowski sum of simplices, and obtain a formula for the volume of P
M
. This gives a combinatorial expression for the degree of an arbitrary torus orbit closure in the Grassmannian Gr
k,n
. We then derive analogous results for the independent set polytope and the underlying flag matroid polytope of M. Our proofs are based on a natural extension of Postnikov’s theory of generalized permutohedra.
- Content Type Journal Article
- DOI 10.1007/s00454-009-9232-9
- Authors
- Federico Ardila, San Francisco State University San Francisco CA USA
- Carolina Benedetti, York University Toronto Canada
- Jeffrey Doker, University of California, Berkeley Berkeley CA USA
- Journal Discrete and Computational Geometry
- Online ISSN 1432-0444
- Print ISSN 0179-5376
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