A Carlitz identity for the wreath product Crn

Chak On Chow, Toufik Mansour

Research output: Contribution to journalArticlepeer-review


We present in this work a new flag major index fmajr for the wreath product Gr,n= Crn, where Cr is the cyclic group of order r and Gn is the symmetric group on n letters. We prove that fmajr is equidistributed with the length function on Gr,n and that the generating function of the pair (desr,fmajr) over Gr,n, where desr is the usual descent number on Gr,n, satisfies a "natural" Carlitz identity, thus unifying and generalizing earlier results due to Carlitz (in the type A case), and Chow and Gessel (in the type B case). A q-Worpitzky identity, a convolution-type recurrence and a q-Frobenius formula are also presented, with combinatorial interpretation given to the expansion coefficients of the latter formula.

Original languageEnglish
Pages (from-to)199-215
Number of pages17
JournalAdvances in Applied Mathematics
Issue number2
StatePublished - Aug 2011


  • Carlitz identity
  • Descent
  • Flag major index
  • Wreath product
  • q-Eulerian polynomial

ASJC Scopus subject areas

  • Applied Mathematics


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