Results 101 to 110 of about 1,852 (188)
On Stirling and bell numbers of order 1/2
FilomatThe Stirling numbers of order 1/2 (of the second kind) introduced by Katugampola are discussed and it is shown that they are given by a scaled subfamily of the generalized Stirling numbers introduced by Hsu and Shiue. This allows to deduce in a straightforward fashion many properties of the Stirling and Bell numbers of order 1/2, for ...
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$B$-Stirling numbers associated to potential polynomials
We introduce the $B$-Stirling numbers of the first and second kind, which are the coefficients of the potential polynomials when we express them in terms of the monomials and the falling factorials, respectively.
Adell, José A., Bényi, Beáta
core
Extended degenerate Stirling numbers of the second kind and extended degenerate Bell polynomials
, 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.
Kim, Taekyun, Kim, Dae San
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Generalizations of Bell number formulas of spivey and Mező
, 2016 We provide q-generalizations of Spivey?s Bell number formula in various settings by considering statistics on different combinatorial structures. This leads to new identities involving q-Stirling numbers of both kinds and q-Lah numbers.
Mark Shattuck
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Partition Statistics and q-Bell Numbers (q = −1)
, 2004 We study three partition statistics and the q-Stirling and q-Bell numbers that serve as their generating functions, evaluating these numbers when q = −1.
Carl G. Wagner
core
An explicit formula for computing Bell numbers in terms of Lah and Stirling numbers
, 2014 3 ...
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, 2014 The r-Bell number B^r(G) of a simple labeled graph G is the number of partitions of its vertex set whose blocks are independent sets of G where the first r-vertices are in different blocks.
Birhanu, Gebrehanna
core
Zeros distribution and interlacing property for certain polynomial sequences
Open MathematicsIn this article, we first prove that the Hankel determinant of order three of the polynomial sequence {Pn(x)=∑k≥0P(n,k)xk}n≥0{\left\{{P}_{n}\left(x)={\sum }_{k\ge 0}P\left(n,k){x}^{k}\right\}}_{n\ge 0} is weakly (Hurwitz) stable, where P(n,k)P\left(n,k ...
Guo Wan-Ming
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On new polynomials related to bell numbers and stirling numbers
Advanced Studies in Theoretical Physics, 2014 H. Y. Lee, C. S. Ryoo
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SHIFTING POWERS IN SPIVEY'S BELL NUMBER FORMULA. [PDF]
Quaest Math, 2022 Mansour T +3 more
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