Geodesic
On \(q\)-boson operators and \(q\)-analogues of the \(r\)-Whitney and \(r\)-Dowling numbers
Journal of integer sequences, Tome 18 (2015) no. 9
We define the $(q, r)$-Whitney numbers of the first and second kinds in terms of the $q$-Boson operators, and obtain several fundamental properties such as recurrence formulas, orthogonality and inverse relations, and other interesting identities. As a special case, we obtain a $q$-analogue of the $r$-Stirling numbers of the first and second kinds. Finally, we define the $(q, r)$-Dowling polynomials in terms of sums of $(q, r)$-Whitney numbers of the second kind, and obtain some of their properties.
Classification : 11B83, 11B73, 05A30
Keywords: Whitney number, Stirling number, boson operator, q-analogue 
@article{JIS_2015__18_9_a6,
     author = {Mangontarum,  Mahid M. and Katriel,  Jacob},
     title = {On \(q\)-boson operators and \(q\)-analogues of the {\(r\)-Whitney} and {\(r\)-Dowling} numbers},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {9},
     zbl = {1402.11031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_9_a6/}
}
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Mangontarum,  Mahid M.; Katriel,  Jacob. On \(q\)-boson operators and \(q\)-analogues of the \(r\)-Whitney and \(r\)-Dowling numbers. Journal of integer sequences, Tome 18 (2015) no. 9. http://geodesic.mathdoc.fr/item/JIS_2015__18_9_a6/