Geodesic
A recurrence relation for the ``inv'' analogue of \(q\)-Eulerian polynomials
The electronic journal of combinatorics, Tome 17 (2010)

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Zbl EuDML
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 
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
@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/}
}
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