On r-Central Incomplete and Complete Bell Polynomials
نویسندگان
چکیده
منابع مشابه
Linear Recurrences for r-Bell Polynomials
Letting Bn,r be the n-th r-Bell polynomial, it is well known that Bn(x) admits specific integer coordinates in the two bases {x}i and {xBi(x)}i according to, respectively, the Stirling numbers and the binomial coefficients. Our aim is to prove that the sequences Bn+m,r(x) and Bn,r+s(x) admit a binomial recurrence coefficient in different bases of the Q-vector space formed by polynomials of Q[X].
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We introduce partial r-Bell polynomials in three combinatorial Hopf algebras. We prove a factorization formula for the generating functions which is a consequence of the Zassenhauss formula. Résumé Les r−polynômes de Bell dans des algèbres de Hopf combinatoires Nous définissons des polynômes r-Bell partiels dans trois algèbres de Hopf combinatoires. Nous prouvons une formule de factorisation po...
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We introduce a family of polynomials that generalizes the Bell polynomials, in connection with the combinatorics of the central moments of the Poisson distribution. We show that these polynomials are dual of the Charlier polynomials by the Stirling transform, and we study the resulting combinatorial identities for the number of partitions of a set into subsets of size at least 2.
متن کاملSome combinatorial formulas for the partial r-Bell polynomials
The partial r-Bell polynomials generalize the classical partial Bell polynomials (coinciding with them when r = 0) by assigning a possibly different set of weights to the blocks containing the r smallest elements of a partition no two of which are allowed to belong to the same block. In this paper, we study the partial r-Bell polynomials from a combinatorial standpoint and derive several new fo...
متن کاملComplete Bell polynomials and new generalized identities for polynomials of higher order
The relations between the Bernoulli and Eulerian polynomials of higher order and the complete Bell polynomials are found that lead to new identities for the Bernoulli and Eulerian polynomials and numbers of higher order. General form of these identities is considered and generating function for polynomials satisfying this general identity is found.
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ژورنال
عنوان ژورنال: Symmetry
سال: 2019
ISSN: 2073-8994
DOI: 10.3390/sym11050724