Results 281 to 290 of about 9,502,067 (333)

Implementation of a Stirling number estimator enables direct calculation of population genetics tests for large sequence datasets

Bioinform., 2018
Motivation Stirling numbers enter into the calculation of several population genetics statistics, including Fu's Fs. However, as alignments become large (>∼50 sequences), the Stirling numbers required rapidly exceed the standard floating point range ...
S. Chen
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Symmetries of Stirling Number Series

The Fibonacci quarterly, 2014
We consider Dirichlet series generated by weighted Stirling numbers, focusing on a symmetry of such series which is reminiscent of a duality relation of negative-order poly-Bernoulli numbers.
P. Young
semanticscholar   +1 more source

Stirling number identities: interconsistency of q-analogues

, 1998
q-analogues of Stirling number identities are formulated, and the interconsistency among the q-analogues of the Stirling numbers and of the binomial coefficients is investigated.
J. Katriel
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Stirling Numbers and Eulerian Numbers

2016
This chapter is dedicated to counting partitions of sets and partitions of sets into cycles, and also introduces Stirling numbers and Bell numbers. As an application of the concepts discussed here we state Faa di Bruno chain rule for the n-th derivative of a composite of n-times differentiable functions on \(\mathbb R\).
Carlo Mariconda, Alberto Tonolo
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A PROBABILISTIC PROOF OF AN IDENTITY RELATED TO THE STIRLING NUMBER OF THE FIRST KIND

, 2009
The basic assumption of the infinite formulation of the secretary problem, originally studied by Gianini and Samuels, is that, if Uj, j = 1, 2,…, is defined as the arrival time of the jth best from an infinite sequence of rankable items, then U1, U2 ...
M. Tamaki
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Stirling number asymptotics from recursion equations using the ray method

, 1991
A technique for computing asymptotic expansions of combinatorial quantities from their recursion relations is presented. It is applied to the Stirling numbers of the first and second kinds, s(n,k) and S(n,k), for n>1 and three ranges of k:(i) k=O(1), (ii)
C. Knessl, J. Keller
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Stirling Numbers for Complex Arguments

SIAM Journal on Discrete Mathematics, 1997
We define the Stirling numbers for complex values and obtain extensions of certain identities involving these numbers. We also show that the generalization is a natural one for proving unimodality and monotonicity results for these numbers. The definition is based on the Cauchy integral formula and can be used for many other combinatorial numbers.
B. RICHMOND, MERLINI, DONATELLA
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Stirling Numbers and Records

1997
Stirling numbers and generalized Stirling numbers and their properties are briefly described first. Then some relationships between Stirling numbers and record times are presented. Finally, we show that generalized Stirling numbers of the first kind describe distributions of some record statistics in the so-called Fα-scheme.
N. Balakrishnan, V. B. Nevzorov
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Stirling Numbers and Bernoulli Numbers

2014
In this chapter we give a formula that describes Bernoulli numbers in terms of Stirling numbers. This formula will be used to prove a theorem of Clausen and von Staudt in the next chapter. As an application of this formula, we also introduce an interesting algorithm to compute Bernoulli numbers.
Masanobu Kaneko, Tomoyoshi Ibukiyama
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A Generalization of the S-Stirling Numbers

Mathematics Magazine, 1956
Introduction: the purpose of this paper is to develope a general formula for the S-Stirling numbers by the use of poly-gama functions. Since the poly-gamma functions have meaning also for non-integer values, we can take the resulting expression for the S-Stirling numbers as their definition.
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