## Abstract

Recently, the q-analog of the harmonic numbers obtained by replacing each positive integer n with n_{q} has been shown to satisfy congruences which generalize Wolstenholme's theorem. Here, we wish to consider further algebraic properties of these numbers. Recall that the r-harmonic, or hyperharmonic, numbers arise by taking repeated partial sums of harmonic numbers. In this paper, we introduce and study properties of a q-analog of the r-harmonic numbers when r = 1. It is defined in terms of a statistic on the set of permutations of length n in which the elements 1,2,...,r belong to distinct cycles (which is enumerated by the r-Stirling number of the first kind).

Original language | English |
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Pages (from-to) | 147-160 |

Number of pages | 14 |

Journal | Afrika Matematika |

Volume | 25 |

Issue number | 1 |

DOIs | |

State | Published - Mar 2014 |

## Keywords

- Harmonic number
- Hyperharmonic number
- q-Generalization

## ASJC Scopus subject areas

- General Mathematics