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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/18111

Title: Function series, Catalan numbers and random walks on trees
Authors: Bajunaid, Ibtesam.
Singman, David.
Cohen, Joel.
Colonna, Flavia.
Keywords: FUNCTION SERIES, CATALAN NUMBERS, RANDOM WALKS
Issue Date: 2005
Publisher: The American Mathematical Monthly
Abstract: The delight of finding unexpected connections is one of the rewards of studying mathematics. In this paper, we link several superficially unrelated entities. We use the generalized Catalan numbers of parameter k as the coefficients of a power series in a certain polynomial of degree k. These series converge and yield continuous–but not differentiable–functions on intervals. These functions turn out to determine the transience of various random walks on trees. They also satisfy functional equations that, by means of the Lagrange-Bürmann inversion formula, lead back to the Catalan numbers.
URI: http://hdl.handle.net/123456789/18111
ISSN: 1930-0972
Appears in Collections:College of Science

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