Some applications of the r-Whitney numbers

Mihoubi, Miloud; Tiachachat, Meriem

doi:10.1016/j.crma.2014.08.001

Cited by 21 publications

(14 citation statements)

References 10 publications

(5 reference statements)

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“…Theorem 26. For n ≥ 0, we have We remark that r-Whitney numbers and their applications were studied by several authors (see [3,4,20]). Note that lim x k,λ , (n ≥ 0), (see [18]),…”

Section: Degenerate Whitney Numbers Of Dowling Latticesmentioning

confidence: 99%

A Study on degenerate Whitney numbers of the first and second kinds of Dowling lattices

Kim,

Kim

2021

Preprint

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Dowling constructed Dowling lattice Q n (G), for any finite set with n elements and any finite multiplicative group G of order m, which is a finite geometric lattice. He also defined the Whitney numbers of the first and second kinds for any finite geometric lattice. These numbers for the Dowling lattice Q n (G) are the Whitney numbers of the first kind V m (n, k) and those of the second kind W m (n, k), which are given by Stirling number-like relations. In this paper, by 'degenerating' such relations we introduce the degenerate Whitney numbers of the first kind and those of the second kind and investigate, among other things, generating functions, recurrence relations and various explicit expressions for them. As further generalizations of the degenerate Whitney numbers of both kinds, we also consider the degenerate r-Whitney numbers of both kinds.

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“…Theorem 26. For n ≥ 0, we have We remark that r-Whitney numbers and their applications were studied by several authors (see [3,4,20]). Note that lim x k,λ , (n ≥ 0), (see [18]),…”

Section: Degenerate Whitney Numbers Of Dowling Latticesmentioning

confidence: 99%

A Study on degenerate Whitney numbers of the first and second kinds of Dowling lattices

Kim,

Kim

2021

Preprint

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“…Let W(n, k; m, r) be the r-Whitney numbers of the second kind [6,8,13,14,[17][18][19][20]28]. Then we have the following identity [16]: W(n, k; m, r) = h n−k (r, m + r, .…”

Section: R-whitney Numbers Of the Second Kind And Their (P Q)-analoguementioning

confidence: 99%

Determinants involving the numbers of the Stirling-type

2019

Filomat

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“…Proof of Theorem 1. Using (21) in the following equation [5,Proposition 15], we have n k=0 n k w k (y) = 1 + y y w n (y) = (−1) n w n (−y − 1) .…”

Section: Proofsmentioning

confidence: 99%

“…The Bernoulli numbers are connected with some well known special numbers [7,8,18,19,20,21]. Rahmani [23] also gave explicit formulas involving different kind of special numbers.…”

Section: Introductionmentioning

confidence: 99%