Euler-Mahonian Statistics on Ordered Partitions and -Meixner Polynomials  

 

Jiang Zeng

Institut Girard Desargues, University Lyon 1, France

Center for Combinatorics, Nankai University, Tianjin, China

zeng@igd.univ-lyon1.fr

 

Abstract.       Full Text PDF

We describe some new Euler-Mahonian statistics on the set of ordered partitions. The distribution of these statistics is closely related to the -Stirling numbers of the second kind and to the moment sequence of -Meixner polynomials. Our proof is based on a continued fraction expansion formula and a generalization of Françon-Viennot’s bijection between some weighted Motzkin paths and permutations. Finally we outline some open problems related to Steingrimsson’s conjectures.