Alternative Proofs on the 2-adic Order of Stirling Numbers of the Second Kind
نویسنده
چکیده
An interesting 2-adic property of the Stirling numbers of the second kind S(n, k) was conjectured by the author in 1994 and proved by De Wannemacker in 2005: ν2(S(2, k)) = d2(k) − 1, 1 ≤ k ≤ 2n. It was later generalized to ν2(S(c2, k)) = d2(k) − 1, 1 ≤ k ≤ 2n, c ≥ 1 by the author in 2009. Here we provide full and two partial alternative proofs of the generalized version. The proofs are based on nonstandard recurrence relations for S(n, k) in the second parameter and congruential identities.
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