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Pré-Publication, Document De Travail Année : 2018

Extensions of partial cyclic orders and consecutive coordinate polytopes

Résumé

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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Dates et versions

ensl-01745941 , version 1 (28-03-2018)
ensl-01745941 , version 2 (29-06-2019)

Identifiants

  • HAL Id : ensl-01745941 , version 1

Citer

Arvind Ayyer, Matthieu Josuat-Vergès, Sanjay Ramassamy. Extensions of partial cyclic orders and consecutive coordinate polytopes. 2018. ⟨ensl-01745941v1⟩

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