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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [23 references]  Display  Hide  Download

https://hal-ens-lyon.archives-ouvertes.fr/ensl-01745941
Contributor : Sanjay Ramassamy <>
Submitted on : Saturday, June 29, 2019 - 12:35:04 PM
Last modification on : Sunday, July 7, 2019 - 11:52:42 PM

File

Cyclic orders and polytopes.pd...
Files produced by the author(s)

Identifiers

  • HAL Id : ensl-01745941, version 2

Citation

Arvind Ayyer, Matthieu Josuat-Vergès, Sanjay Ramassamy. Extensions of partial cyclic orders and consecutive coordinate polytopes. 2019. ⟨ensl-01745941v2⟩

Share

Metrics

Record views

32

Files downloads

30