Discrete & Computational Geometry

, Volume 43, Issue 4, pp 841–854 | Cite as

Matroid Polytopes and their Volumes

  • Federico Ardila
  • Carolina Benedetti
  • Jeffrey Doker


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 Grk,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.

Matroid Matroid polytope Generalized permutahedron Minkowski sum 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Federico Ardila
    • 1
  • Carolina Benedetti
    • 2
  • Jeffrey Doker
    • 3
  1. 1.San Francisco State UniversitySan FranciscoUSA
  2. 2.York UniversityTorontoCanada
  3. 3.University of California, BerkeleyBerkeleyUSA

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