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Closed forms for derangement numbers in terms of the Hessenberg determinants

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In the paper, the authors find closed forms for derangement numbers in terms of the Hessenberg determinants, discover a recurrence relation of derangement numbers, present a formula for any higher order derivative of the exponential generating function of derangement numbers, and compute some related Hessenberg and tridiagonal determinants.

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Acknowledgements

The second author was partially supported by China Postdoctoral Science Foundation with Grant No. 2015M582619. The authors are grateful to the anonymous referees for their careful corrections to and valuable comments on the original version of this paper.

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Authors and Affiliations

  1. Institute of Mathematics, Henan Polytechnic University, Jiaozuo, 454010, Henan, China

    Feng Qi

  2. College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, 028043, Inner Mongolia Autonomous Region, China

    Feng Qi

  3. Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin, 300387, China

    Feng Qi

  4. Department of Mathematics and Informatics, Weinan Normal University, Weinan, 714000, Shaanxi, China

    Jiao-Lian Zhao

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

    Bai-Ni Guo

Authors
  1. Feng Qi
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  2. Jiao-Lian Zhao
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  3. Bai-Ni Guo
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Correspondence to Feng Qi.

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Qi, F., Zhao, JL. & Guo, BN. Closed forms for derangement numbers in terms of the Hessenberg determinants. RACSAM 112, 933–944 (2018). https://doi.org/10.1007/s13398-017-0401-z

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  • DOI: https://doi.org/10.1007/s13398-017-0401-z

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