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Flag enumerations of matroid base polytopes

Abstract : 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 $\textbf{cd}$-index of a polytope can be expressed when a polytope is cut by a hyperplane, and apply these to the $\textbf{cd}$-index of a matroid base polytope of a rank $2$ matroid.
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Sangwook Kim. Flag enumerations of matroid base polytopes. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.283-294. ⟨hal-01185175⟩

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