Stirling numbers of the second kind


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Stirling numbers of the second kind

[¦stər·liŋ ‚nəm·bərz əvthə ′sek·ənd ‚kīnd]
(mathematics)
The numbers S (n, r) giving the numbers of ways that n elements can be distributed among r indistinguishable cells so that no cell remains empty.
References in periodicals archive ?
m](n,k) can be shown to be a kind of generalization of the famous Stirling numbers of the Second kind S(n, k) when the parameter m equals to 1.
The classical Stirling numbers of the second kind can also be obtained from these numbers when [alpha] = 1.
m](n) is known to be a generalization of the classical Bell numbers which is the sum of the Stirling numbers of the second kind S(n, k).
which is the known explicit formula of the Stirling numbers of the second kind.
We give asymptotic expansion of certain sums for generalized 2-associated stirling numbers of the second kind, Bernoulli numbers, Euler numbers by Darboux's method.
Stirling numbers of the second kind S(n, k) can be defined by means of (see [1], [3], [5])
Associated Stirling numbers of the first kind d(n, k) and associated Stirling numbers of the second kind b(n; k) are defined, respectively, by (see [1], [3])
Stirling numbers of the second kind and some problems about it are very interesting research subjects as long, a lot of research results had apparented.
2] Chunyu Du, An Epquation of Stirling Numbers of the Second Kind, Chin.
3] Chun-yu Du, An Identity of Stirling Numbers of the Second Kind, J.
4] Gnmaldi Ralph, A combinatorial identity involving Stirling Numbers of the Second Kind, Util Math.
On some arithmetic properties of polynomial expressions involving Stirling Numbers of the Second Kind, Acta Arith.