On a conjecture of Wilf

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Title: On a conjecture of Wilf
Authors: de Wannemacker, Stefan
Laffey, Thomas
Osburn, Robert
Permanent link: http://hdl.handle.net/10197/7957
Date: Oct-2007
Abstract: Let n and k be natural numbers and let S(n,k) denote the Stirling numbers of the second kind. It is a conjecture of Wilf that the alternating sum [...] is nonzero for all n>2. We prove this conjecture for all n≢2 and ≢2944838 mod 3145728 and discuss applications of this result to graph theory, multiplicative partition functions, and the irrationality of p-adic series.
Type of material: Journal Article
Publisher: Elsevier
Copyright (published version): 2007 Elsevier
Keywords: Stirling numbers of the second kindWilf's conjectureGraph theoryMultiplicative partition functionsP-adic seriesBell numbersGeneralised bellPolynomialsPartitionsMatchings
DOI: 10.1016/j.jcta.2007.01.011
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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