Euler-Mahonian distributions of type B_n

2008/10/29 by Lai, Laurie M., Petersen, T. Kyle
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.0810.5330

Abstract

Adin, Brenti, and Roichman introduced the pairs of statistics (\ndes, \nmaj) and (\fdes, \fmaj). They showed that these pairs are equidistributed over the hyperoctahedral group B_n, and can be considered "Euler-Mahonian" in that they generalize the Carlitz identity. Further, they asked whether there exists a bijective proof of the equidistribution of their statistics. We give such a bijection, along with a new proof of the generalized Carlitz identity.

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