Extensions of partial cyclic orders and consecutive coordinate polytopes - Archive ouverte HAL Access content directly
Journal Articles Annales Henri Lebesgue Year : 2020

Extensions of partial cyclic orders and consecutive coordinate polytopes

(1) , (2, 3) , (4)
1
2
3
4

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.
Fichier principal
Vignette du fichier
Cyclic orders and polytopes.pdf (486.04 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

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

Identifiers

Cite

Arvind Ayyer, Matthieu Josuat-Vergès, Sanjay Ramassamy. Extensions of partial cyclic orders and consecutive coordinate polytopes. Annales Henri Lebesgue, 2020, 3, pp.275-297. ⟨10.5802/ahl.33⟩. ⟨ensl-01745941v2⟩
101 View
109 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More