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Probabilistic Stirling Numbers of the Second Kind and Applications [PDF]

Journal of Theoretical Probability, 2020
Associated with each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided.
José A. Adell
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Study on r-truncated degenerate Stirling numbers of the second kind [PDF]

Open Mathematics, 2022
The degenerate Stirling numbers of the second kind and of the first kind, which are, respectively, degenerate versions of the Stirling numbers of the second kind and of the first kind, appear frequently when we study various degenerate versions of some ...
Kim Taekyun, Kim Dae San, Kim Hyekyung
doaj   +4 more sources

On the Uniqueness Conjecture for the Maximum Stirling Numbers of the Second Kind [PDF]

Results in Mathematics, 2021
The Stirling numbers of the second kind S(n,  k) satisfy S(n, 0)<¿<S(n, kn)=S(n, kn+1)>¿>S(n, n).A long standing conjecture asserts that there exists no n= 3 such that S(n, kn) = S(n, kn+ 1). In this note, we give a characterization of this conjecture in terms of multinomial probabilities, as well as sufficient conditions on n ensuring that
José A. Adell, Daniel Cárdenas-Morales
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Multi-Stirling numbers of the second kind

Filomat, 2023
The multi-Stirling numbers of the second kind, the unsigned multi-Stirling numbers of the first kind, the multi-Lah numbers and the multi-Bernoulli numbers are all defined with the help of the multiple logarithm, and generalize respectively the Stirling ...
Taekyun Kim, Dae San Kim, Hye Jin Kim
semanticscholar   +4 more sources

SOME REMARKS ABOUT STIRLING NUMBERS OF THE SECOND KIND

Human Research in Rehabilitation, 2013
In this paper we give a representation of Stirling numbers of the second kind, we obtain explicit formulas for some cases of Stirling numbers of the second kind and illustrate a method for founding other such formulas.
Ramiz Vugdalić, Fatih Destović
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Computing a family of probabilistic numbers in terms of probabilistic Stirling numbers of the second kind

Applied Mathematics in Science and Engineering
In this paper, we introduce the probabilistic Bernoulli numbers, Cauchy numbers, and Euler numbers of order α associated with the random variable Y, utilizing the generating function approach.
Aimin Xu
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Close Encounters with the Stirling Numbers of the Second Kind [PDF]

Mathematics Magazine, 2012
Summary This is a short introduction to the theory of Stirling numbers of the second kind S(m, k) from the point of view of analysis. It is written as an historical survey centered on the representation of these numbers by a certain binomial transform ...
Khristo N. Boyadzhiev
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On the 2-adic order of Stirling numbers of the second kind and their differences [PDF]

Discrete Mathematics & Theoretical Computer Science, 2009
Let $n$ and $k$ be positive integers, $d(k)$ and $\nu_2(k)$ denote the number of ones in the binary representation of $k$ and the highest power of two dividing $k$, respectively.
Tamás Lengyel
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Some results on p-adic valuations of Stirling numbers of the second kind

AIMS Mathematics, 2020
Let $n$ and $k$ be nonnegative integers. The Stirling number of the second kind, denoted by $S(n, k)$, is defined as the number of ways to partition a set of $n$ elements into exactly $k$ nonempty subsets and we have $$ S(n, k)=\frac{1}{k!}\sum_{i=0}^{k}(
Yulu Feng, Min Qiu
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Beta distribution and associated Stirling numbers of the second kind

Probability and Mathematical Statistics
This article gives a formula for associated Stirling numbers of the second kind based on the moment of a sum of independent random variables having a beta distribution. From this formula we deduce, using probabilistic approaches, lower and upper bounds for these numbers.
Jakub Gismatullin, Patrick Tardivel
semanticscholar   +6 more sources