Some convolution identities and an inverse relation involving partial Bell polynomials

Daniel Birmajer; Juan B. Gil; Michael D. Weiner

doi:10.37236/2476

Some convolution identities and an inverse relation involving partial Bell polynomials

Daniel Birmajer, Juan B. Gil, Michael D. Weiner

Division of Mathematics & Natural Sciences (Altoona)

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We prove an inverse relation and a family of convolution formulas involving par- tial 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 coeffcients. The inverse relation is deduced from a parametrization of suitable identities that facilitate dealing with nested compositions of partial Bell polynomials.

Original language	English (US)
Journal	Electronic Journal of Combinatorics
Volume	19
Issue number	4
DOIs	https://doi.org/10.37236/2476
State	Published - Dec 6 2012

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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abstract = "We prove an inverse relation and a family of convolution formulas involving par- tial 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 coeffcients. The inverse relation is deduced from a parametrization of suitable identities that facilitate dealing with nested compositions of partial Bell polynomials.",

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AB - We prove an inverse relation and a family of convolution formulas involving par- tial 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 coeffcients. The inverse relation is deduced from a parametrization of suitable identities that facilitate dealing with nested compositions of partial Bell polynomials.

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Some convolution identities and an inverse relation involving partial Bell polynomials

Abstract

All Science Journal Classification (ASJC) codes

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