Matroid Polytopes and Their Volumes

Federico Ardila; Carolina Benedetti; Jeffrey Doker

doi:10.46298/dmtcs.2734

Federico Ardila ; Carolina Benedetti ; Jeffrey Doker - Matroid Polytopes and Their Volumes

dmtcs:2734 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2734

Matroid Polytopes and Their VolumesConference paper

Authors: Federico Ardila ¹; Carolina Benedetti ²; Jeffrey Doker ³

1 San Francisco State University
2 Universidad de Los Andes [Mérida, Venezuela]
3 Department of Mathematics [Berkeley]

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 associated flag matroid polytope of $M$ . Our proofs are based on a natural extension of Postnikov's theory of generalized permutohedra.

https://doi.org/10.46298/dmtcs.2734

Source: HAL:hal-01185426v1

Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)

Section: Proceedings

Published on: January 1, 2009

Imported on: January 31, 2017

Keywords: Matroid,generalized permutohedron,matroid polytope,Minkowski sum,mixed volume,flag matroid,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

Funding:

Source : OpenAIRE Graph

Combinatorics in Geometry; Funder: National Science Foundation; Code: 0801075

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