Stirling polynomials
نویسندگان
چکیده
منابع مشابه
Applications of Chromatic Polynomials Involving Stirling Numbers
The Stirling numbers of the second kind, denoted S(n, k), are the number of ways to partition n distinct objects into k nonempty subsets. We use the notation [n] = {1, 2,. . ., n} and sometimes refer to the subsets as blocks. The initial conditions are defined as: S(0, 0) = 1, S(n, 0) = 0, for n ≥ 1, and S(n, k) = 0 for k > n. We also have S(n, 2) = 2 n−1 − 1 and S(n, n − 1) = n 2. The numbers ...
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and Applied Analysis 3 and continuing like that to S8. For large n this method is not convenient. However, later that year Ligowski 4 suggested a better method, providing a generating function for the numbers Sn: e z ∞ ∑ k 0 e k! ∞ ∑ k 0 ∞ ∑ n 0 k k! z n! ∞ ∑ n 0 Sn z n! . 2.4 Further, an effective iteration formula was found Sn n−1 ∑ j 0 ( n − 1 j ) Sj 2.5 by which every Sn can be evaluated st...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1978
ISSN: 0097-3165
DOI: 10.1016/0097-3165(78)90042-0