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.
https://hal-ens-lyon.archives-ouvertes.fr/ensl-01745941 Contributor : Sanjay RamassamyConnect in order to contact the contributor Submitted on : Saturday, June 29, 2019 - 12:35:04 PM Last modification on : Friday, April 1, 2022 - 3:20:02 PM