## Abstract

Axiomatic characterisation of a bibliometric index provides insight into the properties that the index satisfies and facilitates the comparison of different indices. A geometric generalisation of the h-index, called the χ-index, has recently been proposed to address some of the problems with the h-index, in particular, the fact that it is not scale invariant, i.e., multiplying the number of citations of each publication by a positive constant may change the relative ranking of two researchers. While the square of the h-index is the area of the largest square under the citation curve of a researcher, the square of the χ-index, which we call the rec-index (or rectangle-index), is the area of the largest rectangle under the citation curve. Our main contribution here is to provide a characterisation of the rec-index via three properties: monotonicity, uniform citation and uniform equivalence. Monotonicity is a natural property that we would expect any bibliometric index to satisfy, while the other two properties constrain the value of the rec-index to be the area of the largest rectangle under the citation curve. The rec-index also allows us to distinguish between influential researchers who have relatively few, but highly-cited, publications and prolific researchers who have many, but less-cited, publications.

Original language | English |
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Pages (from-to) | 885-896 |

Number of pages | 12 |

Journal | Scientometrics |

Volume | 120 |

Issue number | 2 |

DOIs | |

State | Published - 15 Aug 2019 |

### Bibliographical note

Publisher Copyright:© 2019, Akadémiai Kiadó, Budapest, Hungary.

## Keywords

- Axiomatic characterisation
- Bibliometric index
- Core publications
- Quantity versus quality
- h-index
- rec-index
- χ-index