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INHALE WP3, a multicentre, open-label, pragmatic randomised controlled trial assessing the impact of rapid, ICU-based, syndromic PCR, versus standard-of-care on antibiotic stewardship and clinical outcomes in hospital-acquired and ventilator-associated pneumonia. [PDF]
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A Formula for the Stirling Numbers of the Second Kind
The American Mathematical Monthly, 2020The Stirling number of the second kind S(n, k) is the number of partitions of {1,2,…,n} into k parts and is given by the following explicit formula: (1) S(n,k)=1k!∑j=0k(−1)k−j(kj)jn.
Qiu-Ming Luo, Gao-Wen Xi
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On equal values of Stirling numbers of the second kind
Applied Mathematics and Computation, 2011Abstract S k n denote the Stirling number of the second kind with parameters k and n , i. e. S k n the number of the partition of n elements into k non-empty sets. We formulate the following conjecture concerning the common values of Stirling numbers: Let 1 a b be fixed integers. Then all the solutions of
Ferenczik, Judit +2 more
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On the Location of the Maximum Stirling Number(s) of the Second Kind
Studies in Applied Mathematics, 1978Let S(n, k) denote Stirling numbers of the second kind, and Kn be the integer(s) such that S(n, Kn) ⩾ S(n, k) for all k. We determine the value(s) of Kn to within a maximum error of 1.
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On the Location of the Maximum Stirling Number(s) of the Second Kind [PDF]
The Stirling number of the second kind S(n, k) is the number of ways of partitioning a set of n elements into k nonempty subsets. It is well known that the numbers S(n, k) are unimodal in k, and there are at most two consecutive values K n such that (for fixed n) S(n,K n ) is maximal.
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Simple formulas for Stirling numbers of the second kind
AIP Conference Proceedings, 2015For large values of k, especially those closer to n, the expression for S(n, k), the Stirling numbers (of the second kind) can become quite cumbersome to deal with. In this paper, we obtained simple formulas for S(n, n – r) for small values of r. Our formulas contain only a combination of r combinatorial terms.
A. A. Low, C. K. Ho
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The (r1,...,rp)-Stirling Numbers of the Second Kind
Integers, 2012Abstract ...
Miloud Mihoubi, Mohammed Said Maamra
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A combinatorial generalization of the Stirling Numbers of the second kind
ICECS 2001. 8th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.01EX483), 2002A combinatorial generalization of the Stirling Numbers of the second kind is presented as the number of partitions of a set with n elements in m subsets with at least c elements each. An equivalence with a previous definition is discussed. Combinatorial properties and a recursive relation are obtained.
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