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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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Book ChapterDOI
The Büchi complementation saga
TL;DR: Progress is reviewed on the complementation problem for nondeterministic word automata, which dates back to its introduction in Buchi's seminal 1962 paper, as the subset construction is not sufficient.
Journal ArticleDOI
Asymptotic Development of the Stirling Numbers of the First Kind
Book ChapterDOI
Büchi complementation made tighter
TL;DR: This work describes an improved complementation construction for nondeterministic Buchi automata and analyzes its complexity, showing that the new construction results in an automaton with at most (1.06n) n states, and results in much smaller automata.