A curious polynomial interpolation of Carlitz-Riordan's q-ballot numbers

Contributions to Discrete Mathematics

Frdric Chapoton ; Jiang Zeng

关键词: $q$-Catalan numbers;    lattice paths;    $q$-ballot numbers;   

学科分类：社会科学、人文和艺术（综合）

来源: University of Calgary * Department of Mathematics and Statistics

【 摘 要 】

We study a polynomial sequence $C_n(x|q)$ defined as a solution of a $q$-difference equation. This sequence, evaluated at $q$-integers, interpolates Carlitz--Riordan's $q$-ballot numbers. In the basis given by some kind of $q$-binomial coefficients, the coefficients are again some $q$-ballot numbers. We obtain another curious recurrence relation for these polynomials in a combinatorial way.

【 授权许可】

Unknown