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ARTICLE

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

Siqintuya Jin¹, Bai-Ni Guo^2,*, Feng Qi^3,*

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

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 >

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ARTICLE

On Degenerate Array Type Polynomials

Lan Wu¹, Xue-Yan Chen¹, Muhammet Cihat Dağli², Feng Qi^3,4,*

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

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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