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Reformulations and Generalizations of Hoffman’s and Genčev’s Combinatorial Identities

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Abstract

In the paper, the authors intrinsically observe that Hoffman’s combinatorial identity discovered in 1992 and Genčev’s combinatorial identities extended in 2024 can be reformulated in terms of complete Bell polynomials. They provide alternative proofs and offer some elementary generalizations of these combinatorial identities.

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Acknowledgements

The authors are thankful to Dave L. Renfro (Coralville, IA, USA) for his recommendation of the monograph [5] on 26 October 2023. The authors appreciate the anonymous referees for their valuable comments, helpful suggestions, and careful corrections to the original version of this paper.

Funding

The first author was partially supported by the Key Construction and Characteristic Cultivation Discipline Construction Project of Hulunbuir University (Grant No. 2023XKJS38).

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Authors and Affiliations

  1. School of Mathematics and Physics, Hulunbuir University, Hulunbuir, 021008,, Inner Mongolia, China

    Chun-Ying He

  2. School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, 454010,, Henan, China

    Feng Qi

  3. Independent researcher, University Village, Dallas, TX, 75252, USA

    Feng Qi

Authors
  1. Chun-Ying He
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  2. Feng Qi
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All authors contributed equally to the manuscript and read and approved the final manuscript.

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Correspondence to Feng Qi.

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He, CY., Qi, F. Reformulations and Generalizations of Hoffman’s and Genčev’s Combinatorial Identities. Results Math 79, 131 (2024). https://doi.org/10.1007/s00025-024-02160-0

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