Some convolution identities and an inverse relation involving partial Bell polynomials

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10 Citations (Scopus)

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 languageEnglish (US)
JournalElectronic Journal of Combinatorics
Volume19
Issue number4
StatePublished - Dec 6 2012

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Bell Polynomials
Convolution
Polynomials
Partial
Combinatorial Identities
Parametrization
Chemical analysis
Family

All Science Journal Classification (ASJC) codes

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

Cite this

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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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