Geodesic
Negative $q$-Stirling numbers
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015).

Voir la notice de l'article provenant de la source Episciences

The notion of the negative $q$-binomial was recently introduced by Fu, Reiner, Stanton and Thiem. Mirroring the negative $q$-binomial, we show the classical $q$ -Stirling numbers of the second kind can be expressed as a pair of statistics on a subset of restricted growth words. The resulting expressions are polynomials in $q$ and $(1+q)$. We extend this enumerative result via a decomposition of the Stirling poset, as well as a homological version of Stembridge’s $q=-1$ phenomenon. A parallel enumerative, poset theoretic and homological study for the $q$-Stirling numbers of the first kind is done beginning with de Médicis and Leroux’s rook placement formulation. Letting $t=1+q$ we give a bijective combinatorial argument à la Viennot showing the $(q; t)$-Stirling numbers of the first and second kind are orthogonal. 
@article{DMTCS_2015_special_285_a47,
     author = {Cai, Yue and Readdy, Margaret},
     title = {Negative $q${-Stirling} numbers},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)},
     year = {2015},
     doi = {10.46298/dmtcs.2503},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2503/}
}
TY  - JOUR
AU  - Cai, Yue
AU  - Readdy, Margaret
TI  - Negative $q$-Stirling numbers
JO  - Discrete mathematics & theoretical computer science
PY  - 2015
VL  - DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2503/
DO  - 10.46298/dmtcs.2503
LA  - en
ID  - DMTCS_2015_special_285_a47
ER  - 
%0 Journal Article
%A Cai, Yue
%A Readdy, Margaret
%T Negative $q$-Stirling numbers
%J Discrete mathematics & theoretical computer science
%D 2015
%V DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2503/
%R 10.46298/dmtcs.2503
%G en
%F DMTCS_2015_special_285_a47
Cai, Yue; Readdy, Margaret. Negative $q$-Stirling numbers. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi : 10.46298/dmtcs.2503. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2503/

Cité par Sources :