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Mixed coloured permutations

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Abstract

In this paper, we introduce mixed coloured permutations, permutations with certain coloured cycles, and study the enumerative properties of these combinatorial objects. We derive the generating function, closed forms, recursions and combinatorial identities for the counting sequence, for mixed Stirling numbers of the first kind. In this comprehensive study, we consider further the conditions on the length of the cycles, r-mixed Stirling numbers and the connection to Bell polynomials.

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Acknowledgements

The authors would like to thank the referees for their valuable comments and suggestions that improved the original manuscript greatly in its present form.

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Authors and Affiliations

  1. Faculty of Water Sciences, National University of Public Service, Budapest, Hungary

    Beáta Bényi

  2. Faculty of Agriculture and Animal Science, University of Torbat-e Jam, Torbat-e Jam, Iran

    Daniel Yaqubi

Authors
  1. Beáta Bényi
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  2. Daniel Yaqubi
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Correspondence to Beáta Bényi.

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Communicated by B Sury.

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Bényi, B., Yaqubi, D. Mixed coloured permutations. Proc Math Sci 130, 14 (2020). https://doi.org/10.1007/s12044-019-0546-0

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  • DOI: https://doi.org/10.1007/s12044-019-0546-0

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