A Unified Approach to Generalized Stirling Numbers
Leetsch C. Hsu,Peter J. S. Shiue +1 more
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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.About:
This article is published in Advances in Applied Mathematics.The article was published on 1998-04-01 and is currently open access. It has received 156 citations till now. The article focuses on the topics: Stirling number & Stirling numbers of the first kind.read more
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Poisson-Kingman partitions
TL;DR: In this paper, the authors presented general formulas for random partitions of a finite set derived by Kingman's model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process.
A Bayesian Interpretation of Interpolated Kneser-Ney
TL;DR: A novel interpretation of interpolated Kneser-Ney as approximate inference in a hierarchical Bayesian model consisting of Pitman-Yor processes is proposed.
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A New Formula for the Bernoulli Polynomials
TL;DR: In this paper, a seemingly new class of Stirling-type pairs can be applied to produce a new representation of the Bernoulli polynomials at positive rational arguments.
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Brownian Motion, Bridge, Excursion, and Meander Characterized by Sampling at Independent Uniform Times
TL;DR: In this paper, the joint law of a random process is explicitly described when the process is a Brownian motion, and several new identities involving the laws of these processes are deduced by appropriate conditioning.
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The r-Bell numbers
TL;DR: In this article, the most important combinatorial, algebraic, and analytic properties of generalized Bell numbers are discussed, which in any cases generalize the similar properties of the Bell numbers.
References
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Graph Theory and Its Applications
Jonathan L. Gross,Jay Yellen +1 more
TL;DR: In this article, the authors present a model for drawing graphs and digraphs based on the topology of low dimensions Higher-Order Surfaces and a model of a graph.
Book
The Umbral Calculus
TL;DR: The umbral calculus as mentioned in this paper is an algebraic theory used to study certain types of polynomial functions that play an important role in applied mathematics, and it is a relatively new subject.
Journal ArticleDOI
The Number of Partitions of a Set
TL;DR: The number of partitions of a set has been studied in the context of the number of partitions of sets as mentioned in this paper, and it is shown to be a function of the size of the set.