Geodesic
Flag statistics from the Ehrhart \(h^\ast\)-polynomial of multi-hypersimplices
Guo-Niu Han1 ; Matthieu Josuat-Vergès2
1Université de Strasbourg
2Université de Marne-la-Vallée
The electronic journal of combinatorics, Tome 23 (2016) no. 1
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

It is known that the normalized volume of standard hypersimplices (defined as some slices of the unit hypercube) are the Eulerian numbers. More generally, a recent conjecture of Stanley relates the Ehrhart series of hypersimplices with descents and excedences in permutations. This conjecture was proved by Nan Li, who also gave a generalization to colored permutations. In this article, we give another generalization to colored permutations, using the flag statistics introduced by Foata and Han. We obtain in particular a new proof of Stanley’s conjecture, and some combinatorial identities relating pairs of Eulerian statistics on colored permutations.
DOI : 10.37236/5538
Classification : 05E45, 52B05, 05A05, 11B68, 52B20
Mots-clés : Ehrhart polynomial, descents, Eulerian numbers, colored permutations, hypercube

Guo-Niu Han  1   ; Matthieu Josuat-Vergès  2

1 Université de Strasbourg
2 Université de Marne-la-Vallée 
@article{10_37236_5538,
     author = {Guo-Niu Han and Matthieu Josuat-Verg\`es},
     title = {Flag statistics from the {Ehrhart} \(h^\ast\)-polynomial of multi-hypersimplices},
     journal = {The electronic journal of combinatorics},
     year = {2016},
     volume = {23},
     number = {1},
     doi = {10.37236/5538},
     zbl = {1336.05151},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/5538/}
}
TY  - JOUR
AU  - Guo-Niu Han
AU  - Matthieu Josuat-Vergès
TI  - Flag statistics from the Ehrhart \(h^\ast\)-polynomial of multi-hypersimplices
JO  - The electronic journal of combinatorics
PY  - 2016
VL  - 23
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/5538/
DO  - 10.37236/5538
ID  - 10_37236_5538
ER  - 
%0 Journal Article
%A Guo-Niu Han
%A Matthieu Josuat-Vergès
%T Flag statistics from the Ehrhart \(h^\ast\)-polynomial of multi-hypersimplices
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/5538/
%R 10.37236/5538
%F 10_37236_5538
Guo-Niu Han; Matthieu Josuat-Vergès. Flag statistics from the Ehrhart \(h^\ast\)-polynomial of multi-hypersimplices. The electronic journal of combinatorics, Tome 23 (2016) no. 1. doi: 10.37236/5538

Cité par Sources :