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  • Open Access

    ARTICLE

    Partial Bell Polynomials, Falling and Rising Factorials, Stirling Numbers, and Combinatorial Identities

    Siqintuya Jin1, Bai-Ni Guo2,*, Feng Qi3,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.3, pp. 781-799, 2022, DOI:10.32604/cmes.2022.019941 - 27 June 2022

    Abstract In the paper, the authors collect, discuss, and find out several connections, equivalences, closed-form formulas, and combinatorial identities concerning partial Bell polynomials, falling factorials, rising factorials, extended binomial coefficients, and the Stirling numbers of the first and second kinds. These results are new, interesting, important, useful, and applicable in combinatorial number theory. More >

  • Open Access

    ARTICLE

    On Degenerate Array Type Polynomials

    Lan Wu1, Xue-Yan Chen1, Muhammet Cihat Dağli2, Feng Qi3,4,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.1, pp. 295-305, 2022, DOI:10.32604/cmes.2022.018778 - 24 January 2022

    Abstract In the paper, with the help of the Faá di Bruno formula and an identity of the Bell polynomials of the second kind, the authors define degenerate λ-array type polynomials, establish two explicit formulas, and present several recurrence relations of degenerate λ-array type polynomials and numbers. More >

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