## Abstract

We present in this work a new flag major index fmaj_{r} for the wreath product G_{r},_{n}= C_{rn}, where C_{r} is the cyclic group of order r and G_{n} is the symmetric group on n letters. We prove that fmaj_{r} is equidistributed with the length function on Gr,_{n} and that the generating function of the pair (des_{r},fmaj_{r}) over Gr,_{n}, where des_{r} 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 language | English |
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Pages (from-to) | 199-215 |

Number of pages | 17 |

Journal | Advances in Applied Mathematics |

Volume | 47 |

Issue number | 2 |

DOIs | |

State | Published - Aug 2011 |

## Keywords

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

## ASJC Scopus subject areas

- Applied Mathematics

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