Euler-Mahonian polynomials for C_a \wr S_n

2004/12/05 by Dan Bernstein, Bernstein, Dan
Mathematics · #05A15 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15

paper · pdf · doi:10.48550/arxiv.math/0412091

12 pages

arxiv created 2004/12/05 · arxiv updated 2009/12/01

Abstract

In a recent paper, Regev and Roichman introduced the <_L order and the L-descent number statistic, des_L, on the group of colored permutations, C_a \wr S_n. Here we define the L-reverse major index statistic, rmaj_L, on the same group and study the distribution of des_L and the bi-statistic (des_L, rmaj_L). We obtain new wreath-product analogues of the Eulerian and q-Euler-Mahonian polynomials, and a generalization of Carlitz's identity.

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