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SOME IDENTITIES OF DERANGEMENT NUMBERS

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In combinatorial mathematics, a derangement is a permuta- tion of the elements of a set, such that no element appears in its original position. That is, a derangement is a permutation that has no fixed points. The number of derangements of an n-element set is called the n-th derange- ment number. In this paper, we study some identities involving derange- ment numbers, r-derangement numbers and some other special numbers which are derived from various generating functions.

Abstract

In combinatorial mathematics, a derangement is a permuta- tion of the elements of a set, such that no element appears in its original position. That is, a derangement is a permutation that has no fixed points. The number of derangements of an n-element set is called the n-th derange- ment number. In this paper, we study some identities involving derange- ment numbers, r-derangement numbers and some other special numbers which are derived from various generating functions.

참고문헌 (10)

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  6. 김태균, "DEGENERATE ORDERED BELL NUMBERS AND POLYNOMIALS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 20(2), pp.137~144 (2017), 장전수학회[DOI]
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  9. S. Roman, "The umbral calculus, Pure and Applied Mathematics, 111" (1984), Academic Press, Inc;Harcourt Brace Jovanovich, Publishers
  10. C. Wang, "The r-derangement numbers", Discrete Math., 340(7), pp.1681~1692 (2017)[DOI]

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