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Asymptotic estimates of Stirling numbers
Nico M. Temme
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The article was published on 1992-01-01 and is currently open access. It has received 85 citations till now. The article focuses on the topics: Stirling number & Asymptotic analysis.read more
Citations
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Book
Asymptotic enumeration methods
TL;DR: In this article, the saddle point and large singularities of analytic functions are used for graphical enumeration, including implicit functions, recurrences, and combinations of methods, which are related to our work.
Journal ArticleDOI
A Unified Approach to Generalized Stirling Numbers
Leetsch C. Hsu,Peter J. S. Shiue +1 more
TL;DR: In this article, it was shown that various well-known generalizations of Stirling numbers of the first and second kinds can be unified by starting with transformations between generalized factorials involving three arbitrary parameters.
Journal ArticleDOI
Probabilistic Bounds on the Coefficients of Polynomials with Only Real Zeros
TL;DR: Alignments and approximations for finite sequences, called Polya frequency sequences, which follow from their probabilistic representation are reviewed, finding a number of improvements of known estimates.
Proceedings ArticleDOI
The 3-XORSAT threshold
Olivier Dubois,Jacques Mandler +1 more
TL;DR: In this paper, the existence of the 3-XORSAT threshold was proved and the value of the threshold was established as a function of the root of a transcendental equation.
Journal ArticleDOI
A General Upper Bound for the Satisfiability Threshold of Randomr-SAT Formulae
O Dubois,Y Boufkhad +1 more
TL;DR: A general upper bound of the threshold forr-SAT formulae is established giving a value for 3-S AT of 4.64, significantly improving the previous best upper bound.
References
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Journal ArticleDOI
One integral in three ways: moments of a quantum distribution
TL;DR: In this paper, a generalized harmonic number or polygamma function is used to represent the moments of the exponential probability distribution with parameter in terms of binomial coefficients or Pochhammer symbols.
Proceedings ArticleDOI
Assessing the Significance of Data Mining Results on Graphs with Feature Vectors
TL;DR: This work proposes a novel null model that preserves correlation information between both sources and exploits an adaptive Metropolis sampling and interweaves attribute randomization and graph randomization steps.
Book ChapterDOI
Stirling, bell, bernoulli, euler and eulerian numbers
József Sándor,B. Crstici +1 more
Journal ArticleDOI
On the uniformity of the approximation for $r$-associated Stirling numbers of the second Kind
TL;DR: This work provides a proof of the uniformity of the Hennecart approximation for the associated Stirling numbers, which has been utilized without a proper justification due to the absence of a rigorous proof.
Journal ArticleDOI
Useful properties of the coefficients of the Slevinsky-Safouhi formula for differentiation
TL;DR: Properties of coefficients of the Slevinsky-Safouhi formula are derived, including matrix and orthogonality properties; the characterization of a zero array; generating functions; asymptotics; and recurrence relations for computing a sum as efficiently as possible.