132 research outputs found

    Woon's tree and sums over compositions

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    This article studies sums over all compositions of an integer. We derive a generating function for this quantity, and apply it to several special functions, including various generalized Bernoulli numbers. We connect composition sums with a recursive tree introduced by S.G. Woon and extended by P. Fuchs under the name "general PI tree", in which an output sequence {xn}\{x_n\} is associated to the input sequence {gn}\{g_n\} by summing over each row of the tree built from {gn}\{g_n\}. Our link with the notion of compositions allows to introduce a modification of Fuchs' tree that takes into account nonlinear transforms of the generating function of the input sequence. We also introduce the notion of \textit{generalized sums over compositions}, where we look at composition sums over each part of a composition

    A Continuous Analogue of Lattice Path Enumeration: Part II

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    Here are exhibited some additional results about the continuous binomial coefficients as introduced by L. Cano and R. Diaz in [1].Comment: second versio
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