Results 21 to 30 of about 67,232 (280)
Probabilistic Stirling Numbers of the Second Kind and Applications [PDF]
Journal of Theoretical Probability, 2020 AbstractAssociated 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. Attention, however, is focused on applications. Indeed, such numbers describe the moments of sums of i.i.d.
openaire +5 more sources
Degenerate Derangement Polynomials and Numbers
Fractal and Fractional, 2021 In this paper, we consider a new type of degenerate derangement polynomial and number, which shall be called the degenerate derangement polynomials and numbers of the second kind.
Minyoung Ma, Dongkyu Lim
doaj +1 more source
Combinatorial Diophantine equations and a refinement of a theorem on separated variables equations [PDF]
, 2013 We look at Diophantine equations arising from equating classical counting functions such as perfect powers, binomial coefficients and Stirling numbers of the first and second kind.
Bilu, Yuri F. +3 more
core +2 more sources
Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering
Journal of Mathematics, 2022 Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via boson operators ...
Taekyun Kim, Dae San Kim, Hye Kyung Kim
doaj +1 more source
Some Symmetric Identities Involving the Stirling Polynomials Under the Finite Symmetric Group
Mathematics, 2018 In the paper, the authors present some symmetric identities involving the Stirling polynomials and higher order Bernoulli polynomials under all permutations in the finite symmetric group of degree n.
Dongkyu Lim, Feng Qi
doaj +1 more source
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
doaj +1 more source
R(p,q)- analogs of discrete distributions: general formalism and application [PDF]
, 2019 In this paper, we define and discuss $\mathcal{R}(p,q)$- deformations of basic univariate discrete distributions of the probability theory. We mainly focus on binomial, Euler, P\'olya and inverse P\'olya distributions.
Hounkonnou, Mahouton Norbert +1 more
core +3 more sources
Maximum Stirling Numbers of the Second Kind
, 2008 See the abstract in the attached ...
G. KEMKES +2 more
openaire +3 more sources
THE 2-ADIC VALUATIONS OF STIRLING NUMBERS OF THE SECOND KIND [PDF]
International Journal of Number Theory, 2012 In this paper, we investigate the 2-adic valuations of the Stirling numbers S(n, k) of the second kind. We show that v2(S(4i, 5)) = v2(S(4i + 3, 5)) if and only if i ≢ 7 (mod 32). This confirms a conjecture of Amdeberhan, Manna and Moll raised in 2008. We show also that v2(S(2n+ 1, k + 1)) = s2(n) - 1 for any positive integer n, where s2(n) is the sum ...
Hong, Shaofang +2 more
openaire +2 more sources
Study on r-truncated degenerate Stirling numbers of the second kind
Open Mathematics, 2022 Abstract 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 special numbers and polynomials. The aim of this article is to consider the r-
Kim Taekyun, Kim Dae San, Kim Hyekyung
openaire +3 more sources