Flag enumerations of matroid base polytopes

In this paper, we study flag structures of matroid base polytopes. We describe faces of matroid base polytopes in terms of matroid data, and give conditions for hyperplane splits of matroid base polytopes. Also, we show how the cd -index of a polytope can be expressed when a polytope is cut by a hyperplane, and apply these to the cd -index of a matroid base polytope of a rank 2 matroid. Resume. Dans cet article, nous etudions les structures de drapeau de polytopes de base de matroide. Nous decrivons des faces de polytopes de base de matroide en terme des donnees de matroide, et donner des conditions pour les divisions de hyperplane de polytopes de base de matroide. Aussi, nous montrons comment le cd -index d'un polytope peut etre exprime' quand un polytope est coupe par un hyperplane, et s'appliquer ceux-ci au cd -index d'un polytope de base de matroide d'un rang 2 matroide.

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