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Identities for partial Bell polynomials derived from identities for weighted integer compositions

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Abstract

We discuss closed-form formulas for the (n, k)th partial Bell polynomials derived in Cvijović (Appl Math Lett 24:1544–1547, 2011). We show that partial Bell polynomials are special cases of weighted integer compositions, and demonstrate how the identities for partial Bell polynomials easily follow from more general identities for weighted integer compositions. We also provide short and elegant probabilistic proofs of the latter, in terms of sums of discrete integer-valued random variables. Finally, we outline further identities for the partial Bell polynomials.

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  1. Department of Computer Science and Mathematics, Goethe-Universität Frankfurt am Main, P.O. Box 154, Robert-Mayer-Straße 10, 60325, Frankfurt am Main, Germany

    Steffen Eger

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  1. Steffen Eger
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Correspondence to Steffen Eger.

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Eger, S. Identities for partial Bell polynomials derived from identities for weighted integer compositions. Aequat. Math. 90, 299–306 (2016). https://doi.org/10.1007/s00010-015-0338-2

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  • DOI: https://doi.org/10.1007/s00010-015-0338-2

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