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A q-analog of Schläfli and Gould identities on Stirling numbers

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Abstract

Stirling numbers of both kinds are linked to each other via two combinatorial identities due to Schläfli and Gould. Using q-analogs of Stirling numbers defined as inversion generating functions, we provide q-analogs of the two identities. The proof is computational and we leave open the problem of finding a more combinatorial one.

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Authors and Affiliations

  1. CNRS and Institut Gaspard Monge, Université Paris-Est Marne-la-Vallée, Champs-sur-Marne, France

    Matthieu Josuat-Vergès

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  1. Matthieu Josuat-Vergès
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Correspondence to Matthieu Josuat-Vergès.

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Supported by Agence Nationale de la Recherche ANR CARMA (ANR-12-BS01-0017).

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Josuat-Vergès, M. A q-analog of Schläfli and Gould identities on Stirling numbers. Ramanujan J 46, 483–507 (2018). https://doi.org/10.1007/s11139-017-9885-6

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  • DOI: https://doi.org/10.1007/s11139-017-9885-6

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