Geodesic
A \(p,q\)-analogue of a formula of Frobenius
The electronic journal of combinatorics, Tome 10 (2003)

Voir la notice de l'article provenant de la source The Electronic Journal of Combinatorics website

Zbl EuDML
Garsia and Remmel (JCT. A 41 (1986), 246-275) used rook configurations to give a combinatorial interpretation to the $q$-analogue of a formula of Frobenius relating the Stirling numbers of the second kind to the Eulerian polynomials. Later, Remmel and Wachs defined generalized $p,q$-Stirling numbers of the first and second kind in terms of rook placements. Additionally, they extended their definition to give a $p,q$-analogue of rook numbers for arbitrary Ferrers boards. In this paper, we use Remmel and Wach's definition and an extension of Garsia and Remmel's proof to give a combinatorial interpretation to a $p,q$-analogue of a formula of Frobenius relating the $p,q$-Stirling numbers of the second kind to the trivariate distribution of the descent number, major index, and comajor index over $S_n$. We further define a $p,q$-analogue of the hit numbers, and show analytically that for Ferrers boards, the $p,q$-hit numbers are polynomials in $(p,q)$ with nonnegative coefficients.
DOI : 10.37236/1702
Classification : 05A30, 05A05, 05A19, 05A18 
Karen S. Briggs; Jeffrey B. Remmel. A \(p,q\)-analogue of a formula of Frobenius. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1702
@article{10_37236_1702,
     author = {Karen S. Briggs and Jeffrey B. Remmel},
     title = {A \(p,q\)-analogue of a formula of {Frobenius}},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1702},
     zbl = {1011.05010},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1702/}
}
TY  - JOUR
AU  - Karen S. Briggs
AU  - Jeffrey B. Remmel
TI  - A \(p,q\)-analogue of a formula of Frobenius
JO  - The electronic journal of combinatorics
PY  - 2003
VL  - 10
UR  - http://geodesic.mathdoc.fr/articles/10.37236/1702/
DO  - 10.37236/1702
ID  - 10_37236_1702
ER  - 
%0 Journal Article
%A Karen S. Briggs
%A Jeffrey B. Remmel
%T A \(p,q\)-analogue of a formula of Frobenius
%J The electronic journal of combinatorics
%D 2003
%V 10
%U http://geodesic.mathdoc.fr/articles/10.37236/1702/
%R 10.37236/1702
%F 10_37236_1702

Cité par Sources :