  Dowling showed that the Whitney numbers of the first kind and of the second
kind satisfy Stirling number-like relations. Recently, Kim-Kim introduced the
degenerate r-Whitney numbers of the first kind and of the second kind, as
degenerate versions and further generalizations of the Whitney numbers of both
kinds. The normal ordering of an integral power of the number operator in terms
of boson operators is expressed with the help of the Stirling numbers of the
second kind. In this paper, it is noted that the normal ordering of a certain
quantity involving the number operator is expressed in terms of the degenerate
r-Whitney numbers of the second kind. We derive some properties, recurrence
relations, orthogonality relations and several identities on those numbers from
such normal ordering. In addition, we consider the degenerate r-Dowling
polynomials as a natural extension of the degenerate r-Whitney numbers of the
second kind and investigate their properties.
