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- W2621117104 abstract "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 ${x_n}$ is associated to the input sequence ${g_n}$ by summing over each row of the tree built from ${g_n}$. 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." @default.
- W2621117104 created "2017-06-09" @default.
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- W2621117104 date "2018-01-01" @default.
- W2621117104 modified "2023-10-17" @default.
- W2621117104 title "Woon’s tree and sums over compositions" @default.
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- W2621117104 hasPublicationYear "2018" @default.
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