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.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     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},
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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/