The lattice of flats and its underlying flag matroid polytope

1997 ◽  
Vol 1 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Alexandre V. Borovik ◽  
Israel M. Gelfand ◽  
Andrew Vince ◽  
Neil White
Keyword(s):  
Matroid Polytope

scholarly journals Valuations for Matroid Polytope Subdivisions

2010 ◽  
Vol 62 (6) ◽  
pp. 1228-1245 ◽  
Author(s):  
Federico Ardila ◽  
Alex Fink ◽  
Felipe Rincón
Keyword(s):  
Matroid Polytope ◽  
Matroid Polytopes

AbstractWe prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.

scholarly journals On the cardinality constrained matroid polytope

Networks ◽  
2011 ◽  
Vol 57 (3) ◽  
pp. 240-246 ◽  
Author(s):  
Jean François Maurras ◽  
Rüdiger Stephan
Keyword(s):  
Matroid Polytope

scholarly journals Determining a matroid polytope by non-Radon partitions

1987 ◽  
Vol 94 ◽  
pp. 55-60 ◽  
Author(s):  
Raul Cordovil ◽  
Ilda P. Silva
Keyword(s):  
Matroid Polytope

scholarly journals Matroid Polytopes and Their Volumes

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Federico Ardila ◽  
Carolina Benedetti ◽  
Jeffrey Doker
Keyword(s):  
Natural Extension ◽  
Independent Set ◽  
Minkowski Sum ◽  
Orbit Closure ◽  
Matroid Polytope ◽  
Matroid Polytopes ◽  
International Audience ◽  
Combinatorial Expression

International audience 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. On exprime le polytope matroïde $P_M$ d'un matroïde $M$ comme somme signée de Minkowski de simplices, et on obtient une formule pour le volume de $P_M$. Ceci donne une expression combinatoire pour le degré d'une clôture d'orbite de tore dans la Grassmannienne $Gr_{k,n}$. Ensuite, on déduit des résultats analogues pour le polytope ensemble indépendant et pour le polytope matroïde drapeau associé à $M$. Nos preuves sont fondées sur une extension naturelle de la théorie de Postnikov de permutoèdres généralisés.

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