Geodesic
Statistics on Lattice Walks and q-Lassalle 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

This paper contains two results. First, I propose a $q$-generalization of a certain sequence of positive integers, related to Catalan numbers, introduced by Zeilberger, see Lassalle (2010). These $q$-integers are palindromic polynomials in $q$ with positive integer coefficients. The positivity depends on the positivity of a certain difference of products of $q$-binomial coefficients.To this end, I introduce a new inversion/major statistics on lattice walks. The difference in $q$-binomial coefficients is then seen as a generating function of weighted walks that remain in the upper half-plan. 
@article{DMTCS_2015_special_285_a72,
     author = {Tevlin, Lenny},
     title = {Statistics on {Lattice} {Walks} and {q-Lassalle} {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.2528},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2528/}
}
TY  - JOUR
AU  - Tevlin, Lenny
TI  - Statistics on Lattice Walks and q-Lassalle 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.2528/
DO  - 10.46298/dmtcs.2528
LA  - en
ID  - DMTCS_2015_special_285_a72
ER  - 
%0 Journal Article
%A Tevlin, Lenny
%T Statistics on Lattice Walks and q-Lassalle 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.2528/
%R 10.46298/dmtcs.2528
%G en
%F DMTCS_2015_special_285_a72
Tevlin, Lenny. Statistics on Lattice Walks and q-Lassalle 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.2528. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2528/

Cité par Sources :