Some Convolution Identities and an Inverse Relation Involving Partial Bell Polynomials

We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting multinomial formula for the binomial coefficients. The inverse relatio...

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Bibliographic Details
Published in:The Electronic journal of combinatorics 2012-12, Vol.19 (4)
Main Authors: Birmajer, Daniel, Gil, Juan B., Weiner, Michael D.
Format: Article
Language:English
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Summary:We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting multinomial formula for the binomial coefficients. The inverse relation is deduced from a parametrization of suitable identities that facilitate dealing with nested compositions of partial Bell polynomials.
ISSN:1077-8926
1077-8926
DOI:10.37236/2476