Complementary Bell Numbers: Arithmetical Properties and Wilf’s Conjecture

Tewodros Amdeberhan (), Valerio De Angelis () and Victor H. Moll ()
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Tewodros Amdeberhan: Tulane University, Department of Mathematics
Valerio De Angelis: Xavier University of Louisiana, Department of Mathematics
Victor H. Moll: Tulane University, Department of Mathematics

A chapter in Advances in Combinatorics, 2013, pp 23-56 from Springer

Abstract: Abstract The 2-adic valuations of Bell and complementary Bell numbers are determined. The complementary Bell numbers are known to be zero at n = 2 and H. S. Wilf conjectured that this is the only case where vanishing occurs. N. C. Alexander and J. An proved (independently) that there are at most two indices where this happens. This paper presents yet an alternative proof of the latter.

Keywords: Valuations; Bell numbers; Complementary Bell numbers; Closed-form summation; Wilf’s conjecture (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-30979-3_2

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DOI: 10.1007/978-3-642-30979-3_2

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