The 2-adic valuation of Stirling numbers. (English) Zbl 1218.11024

Summary: We analyze properties of the 2-adic valuations of \(S(n,k)\), the Stirling numbers of the second kind. For fixed \(k \in \mathbb{N}\), a conjectured pattern for the valuation is provided in terms of the dyadic format of \(n\). This conjecture is established for \(k=5\).


11B73 Bell and Stirling numbers
11B50 Sequences (mod \(m\))
05A15 Exact enumeration problems, generating functions
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