Close Encounters with the Stirling Numbers of the Second Kind

Boyadzhiev, Khristo N.

doi:10.4169/math.mag.85.4.252

Cited by 80 publications

(44 citation statements)

References 9 publications

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“…This is a generalisation of the work done in [6]. (1−x(e t −1)) r , for instance in [7,10,11,12,14,15,16,17,18,21]. Hence, our results in Theorem 3.1 offers a generalised combinatorial interpretation of these geometric polynomials.…”

Section: When Multiple Bars Are Consideredsupporting

confidence: 77%

“…Part II of [9]). These polynomials are well known in the literature, and it is also well known that these polynomials arise from variations of the generating function e rt (1−x(e t −1)) r , for instance in [7,10,11,12,14,15,16,17,18,21]. In this study our combinatorial interpretation of the integer sequences arising from the generating function…”

Section: Geometric Polynomials Go Far Back As Euler's Work On the Yeamentioning

confidence: 82%

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A combinatorial analysis of higher order generalised geometric polynomials: A generalisation of barred preferential arrangements

Nkonkobe

Bényi

Corcino

et al. 2020

Discrete Mathematics

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A barred preferential arrangement is a preferential arrangement, onto which in-between the blocks of the preferential arrangement a number of identical bars are inserted. We offer a generalisation of barred preferential arrangements by making use of the generalised Stirling numbers proposed by Hsu and Shiue (1998). We discuss how these generalised barred preferential arrangements offer a unified combinatorial interpretation of geometric polynomials. We also discuss asymptotic properties of these numbers.Mathematics Subject Classifications : 05A15, 05A16, 05A18, 05A19, 11B73, 11B83 Keyword(s):preferential arrangement, barred preferential arrangement, geometric polynomial.

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Section: When Multiple Bars Are Consideredsupporting

confidence: 77%

Section: Geometric Polynomials Go Far Back As Euler's Work On the Yeamentioning

confidence: 82%

A combinatorial analysis of higher order generalised geometric polynomials: A generalisation of barred preferential arrangements

Nkonkobe

Bényi

Corcino

et al. 2020

Discrete Mathematics

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“…Bell called them “exponential polynomials,” so did Touchard . They were called exponential polynomials also by Rota and by Boyadzhiev . Touchard has no much contribution to the theory.…”

Section: More Remarksmentioning

confidence: 99%

“…15,51,52 They were called exponential polynomials also by Rota 53 and by Boyadzhiev. 46,47,[54][55][56][57] Touchard has no much contribution to the theory. Most properties were found by Grunert, Bell, and, for example, in the papers.…”

Section: More Remarksmentioning

confidence: 99%

Some properties and an application of multivariate exponential polynomials

Niu

Lim

et al. 2020

Math Methods in App Sciences

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In the paper, the authors introduce a notion “multivariate exponential polynomials” which generalize exponential numbers and polynomials, establish explicit formulas, inversion formulas, and recurrence relations for multivariate exponential polynomials in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, two identities for the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds, construct some determinantal inequalities and product inequalities for multivariate exponential polynomials with the aid of some properties of completely monotonic functions and other known results, derive the logarithmic convexity and logarithmic concavity for multivariate exponential polynomials, and finally find an application of multivariate exponential polynomials to white noise distribution theory by confirming that multivariate exponential polynomials satisfy conditions for sequences required in white noise distribution theory.

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“…It is known that, for n m 0, S(n, m) can be computed by the explicit formula (also discussed in [12]) (see [1,13,16,19]; and the references cited therein).…”

Section: Introductionmentioning

confidence: 99%