Geodesic
A recurrence relation for the ``inv'' analogue of \(q\)-Eulerian polynomials
The electronic journal of combinatorics, Tome 17 (2010)
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We study in the present work a recurrence relation, which has long been overlooked, for the $q$-Eulerian polynomial $A_n^{{\rm des},{\rm inv}}(t,q) =\sum_{\sigma\in\mathfrak{S}_n} t^{{\rm des}(\sigma)}q^{{\rm inv}(\sigma)}$, where ${\rm des}(\sigma)$ and ${\rm inv}(\sigma)$ denote, respectively, the descent number and inversion number of $\sigma$ in the symmetric group $\mathfrak{S}_n$ of degree $n$. We give an algebraic proof and a combinatorial proof of the recurrence relation.
DOI : 10.37236/471
Classification : 05A05, 05A15 
@article{10_37236_471,
     author = {Chak-On Chow},
     title = {A recurrence relation for the ``inv'' analogue of {\(q\)-Eulerian} polynomials},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/471},
     zbl = {1189.05005},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/471/}
}
TY  - JOUR
AU  - Chak-On Chow
TI  - A recurrence relation for the ``inv'' analogue of \(q\)-Eulerian polynomials
JO  - The electronic journal of combinatorics
PY  - 2010
VL  - 17
UR  - http://geodesic.mathdoc.fr/articles/10.37236/471/
DO  - 10.37236/471
ID  - 10_37236_471
ER  - 
%0 Journal Article
%A Chak-On Chow
%T A recurrence relation for the ``inv'' analogue of \(q\)-Eulerian polynomials
%J The electronic journal of combinatorics
%D 2010
%V 17
%U http://geodesic.mathdoc.fr/articles/10.37236/471/
%R 10.37236/471
%F 10_37236_471
Chak-On Chow. A recurrence relation for the ``inv'' analogue of \(q\)-Eulerian polynomials. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/471

Cité par Sources :