On q-Boson Operators and q-Analogues of the r-Whitney and r-Dowling Numbers
نویسندگان
چکیده
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.
منابع مشابه
Some Theorems and Applications of the (q, r)-Whitney Numbers
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 ...
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