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Discrete Mathematics & Theoretical Computer Science |
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.2734Matroid Polytopes and Their VolumesArticle
- 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.
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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