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Extensions of partial cyclic orders and consecutive coordinate polytopes

Abstract : We introduce several classes of polytopes contained in [0, 1] n and cut out by inequalities involving sums of consecutive coordinates , extending a construction by Stanley. We show that the normalized volumes of these polytopes enumerate the extensions to total cyclic orders of certains classes of partial cyclic orders. We also provide a combinatorial interpretation of the Ehrhart h *-polynomials of some of these polytopes in terms of descents of total cyclic orders. The Euler numbers, the Eulerian numbers and the Narayana numbers appear as special cases.
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Submitted on : Saturday, June 29, 2019 - 12:35:04 PM
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Arvind Ayyer, Matthieu Josuat-Vergès, Sanjay Ramassamy. Extensions of partial cyclic orders and consecutive coordinate polytopes. Annales Henri Lebesgue, UFR de Mathématiques - IRMAR, 2020, 3, pp.275-297. ⟨10.5802/ahl.33⟩. ⟨ensl-01745941v2⟩

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