, 2020 Bell and Stirling numbers of first and second kind tell the number of ways that n objects, or n cycles in the case of Stirling numbers of first kind, can be distributed in k cells. They are usually obtained through recurrence rules. However, recurrence rules only tell how many distributions are possible, not the specific form of each distribution, so ...
Giuseppe Tavazza
openalex +2 more sources
Extended degenerate Stirling numbers of the second kind and extended degenerate Bell polynomials [PDF]
, 2017 In a recent work, the degenerate Stirling polynomials of the second kind were studied by T. Kim. In this paper, we investigate the extended degenerate Stirling numbers of the second kind and the extended degenerate Bell polynomials associated with them.
Taekyun Kim, Dae San Kim
openalex +3 more sources
Probabilistic Poly Degenerate r-Stirling Numbers of the Second Kind and r-Bell Polynomials
European Journal of Pure and Applied MathematicsWe introduce degenerate poly r-Stirling numbers of the second kind and poly r-Bell polynomials by using degenerate polyexponential function and investigate some properties of these number and polynomials.
S. H. Lee
openalex +3 more sources
EVOLUTIONARY MATHEMATICS AND SCIENCE FOR GENERAL FAMOUS NUMBERS: STIRLING-EULER-LAH-BELL
, 2021 We first introduce Pascal, Stirling, Eulerian, Lah and Bell numbers via sorting, then generalize Stirling numbers of both kinds [■(n@k)], {■(n@k)}, Eulerian numbers of two orders 〈■(n@k)〉, 〈〈■(n@k)〉 〉, Lah numbers L(n,k)=∑_(j=1)^n▒[■(n@j)] {■(j@k)} and ∑_(k=0)^(n-1)▒〖2^k 〈■(n@k)〉 〗=∑_(k=1)^n▒(∑_(j-1)^(k+1)▒[■(k+1@j)] ){■(n@k)} , the right-hand side of ...
Leon Chang +2 more
openalex +2 more sources
BELL, BERNOULLI, CAUCHY, HARMONIC AND STIRLING NUMBERS
Algebras Groups and Geometries, 2023 S. Vidal‐Beltrán +3 more
openalex +2 more sources
Partial Bell Polynomials, Falling and Rising Factorials, Stirling Numbers, and Combinatorial Identities [PDF]
Computer Modeling in Engineering & Sciences, 2022 Siqintuya Jin, Bai‐Ni Guo, Feng Qi
openalex +2 more sources
On some congruences for the Bell numbers and for the Stirling numbers
Journal of Number Theory, 1991 AbstractWe shall give some congruences for the Bell numbers, and for the Stirling numbers, by investigating the elementary properties of p-adic integrals.
Hirofumi Tsumura
openalex +2 more sources
q -Stirling numbers of the second kind and q -Bell numbers for graphs
Electronic Notes in Discrete Mathematics, 2016 Stirling numbers of the second kind and Bell numbers for graphs were defined by Duncan and Peele in 2009. In a previous paper, one of us, jointly with Nyul, extended the known results for these special numbers by giving new identities, and provided a list of explicit expressions for Stirling numbers of the second kind and Bell numbers for particular ...
Zsófia R. Kereskényiné Balogh +1 more
openalex +3 more sources
Probabilistic degenerate r-Stirling numbers of the second and probabilistic degenerate r-Bell polynomials [PDF]
Assume that Y is a random variable whose moment generating function exists in a neighborhood of the origin. We study the probabilistic degenerate r-Stirling numbers of the second kind associated with Y and the probabilistic degenerate r-Bell polynomials associated with Y.
T. Kim, Dae San Kim
openalex +3 more sources
The r-Bell numbers and matrices containing non-central Stirling and Lah numbers
Journal of Mathematics and Computer Science, 2019 Roberto B. Corcino +3 more
openalex +3 more sources