On the p-adic valuation of stirling numbers of the first kind
نویسندگان
چکیده
منابع مشابه
The 2-adic Valuation of Stirling Numbers
We analyze properties of the 2-adic valuations of S(n, k), the Stirling numbers of the second kind. A conjecture that describes patterns of these valuations for fixed k and n modulo powers of 2 is presented. The conjecture is established for k = 5.
متن کاملThe 2-adic Valuation of Stirling Numbers of the Second Kind
In this paper, we investigate the 2-adic valuation of the Stirling numbers S(n, k) of the second kind. We show 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. This confirms a conjecture of Amdeberhan, Manna and Moll. We show also that v2(S(4i, 5)) = v2(S(4i + 3, 5)) if and only if i 6≡ 7 (mod 32). This proves another conjecture of ...
متن کاملConvolution Properties of the Generalized Stirling Numbers and the Jacobi-Stirling Numbers of the First Kind
In this paper, we establish several properties of the unified generalized Stirling numbers of the first kind, and the Jacobi-Stirling numbers of the first kind, by means of the convolution principle of sequences. Obtained results include generalized Vandermonde convolution for the unified generalized Stirling numbers of the first kind, triangular recurrence relation for general Stirling-type nu...
متن کاملAsymptotic Expansions for the Stirling Numbers of the First Kind
Let s(n,m) denote the (unsigned) Stirling numbers of the first kind: s(n,m) := [w] (w(w + 1) · · · (w + n− 1)) (1 ≤ m ≤ n, n ≥ 1). Many different asymptotic expressions for s(n,m), as n→∞, have been proposed in the literature due to their wide applications, cf. Temme [8] for a brief survey of known results together with a uniform asymptotic expansion valid for all m, 1 ≤ m ≤ n. Recently, Wilf [...
متن کاملthe effect of taftan pozzolan on the compressive strength of concrete in the environmental conditions of oman sea (chabahar port)
cement is an essential ingredient in the concrete buildings. for production of cement considerable amount of fossil fuel and electrical energy is consumed. on the other hand for generating one tone of portland cement, nearly one ton of carbon dioxide is released. it shows that 7 percent of the total released carbon dioxide in the world relates to the cement industry. considering ecological issu...
ذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Mathematica Hungarica
سال: 2016
ISSN: 0236-5294,1588-2632
DOI: 10.1007/s10474-016-0680-4