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- Title
THE 2-ADIC VALUATIONS OF STIRLING NUMBERS OF THE SECOND KIND.
- Authors
HONG, SHAOFANG; ZHAO, JIANRONG; ZHAO, WEI
- Abstract
In this paper, we investigate the 2-adic valuations of the Stirling numbers S(n, k) of the second kind. We show that v2(S(4i, 5)) = v2(S(4i + 3, 5)) if and only if i ≢ 7 (mod 32). This confirms a conjecture of Amdeberhan, Manna and Moll raised in 2008. We show also that v2(S(2n + 1, k + 1)) = s2(n) - 1 for any positive integer n, where s2(n) is the sum of binary digits of n. It proves another conjecture of Amdeberhan, Manna and Moll.
- Subjects
GRAPH labelings; NUMBER theory; VALUATION theory; PARTITIONS (Mathematics); NATURAL numbers; LOGICAL prediction
- Publication
International Journal of Number Theory, 2012, Vol 8, Issue 4, p1057
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042112500625