Geodesic
Some theorems and applications of the \((q,r)\)-Whitney numbers
Journal of integer sequences, Tome 20 (2017) no. 2
The $(q,r)$-Whitney numbers were recently defined in terms of the $q$-Boson operators, and several combinatorial properties which appear to be $q$-analogues of similar properties were studied. In this paper, we obtain elementary and complete symmetric polynomial forms for the $(q,r)$-Whitney numbers, and give combinatorial interpretations in the context of $A$-tableaux. We also obtain convolution-type identities using the combinatorics of $A$-tableaux. Lastly, we present applications and theorems related to discrete $q$-distributions.
Classification : 11B83, 11B73, 05A30
Keywords: (q, r)-Whitney number, symmetric function, A-tableau, q-distribution 
@article{JIS_2017__20_2_a3,
     author = {Mangontarum,  Mahid M.},
     title = {Some theorems and applications of the {\((q,r)\)-Whitney} numbers},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {2},
     zbl = {1420.11055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_2_a3/}
}
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Mangontarum,  Mahid M. Some theorems and applications of the \((q,r)\)-Whitney numbers. Journal of integer sequences, Tome 20 (2017) no. 2. http://geodesic.mathdoc.fr/item/JIS_2017__20_2_a3/