Extensions of partial cyclic orders and consecutive coordinate polytopes

Arvind Ayyer; Matthieu Josuat-Vergès; Sanjay Ramassamy

doi:10.5802/ahl.33

Journal articles

Extensions of partial cyclic orders and consecutive coordinate polytopes

Arvind Ayyer ¹ Matthieu Josuat-Vergès ^{2, 3} Sanjay Ramassamy ⁴

1 Department of Mathematics, Indian Institute of Science

2 LIGM - Laboratoire d'Informatique Gaspard-Monge

3 CNRS - Centre National de la Recherche Scientifique

4 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

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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Journal articles

Domain :

Mathematics [math] / Combinatorics [math.CO]

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Submitted on : Saturday, June 29, 2019 - 12:35:04 PM
Last modification on : Friday, April 1, 2022 - 3:20:02 PM

Extensions of partial cyclic orders and consecutive coordinate polytopes

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Extensions of partial cyclic orders and consecutive coordinate polytopes

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