  Broder introduced the r-Stirling numbers of the first kind and of the second
kind which enumerate restricted permutations and respectively restricted
partitions, the restriction being that the first r elements must be in distinct
cycles and respectively in distinct subsets. Kim-Kim-Lee-Park constructed the
degenerate r-Stirling numbers of both kinds as degenerate versions of them. The
aim of this paper is to derive some identities and recurrence relations for the
degenerate r-Stirling numbers of the first kind and of the second kind via
boson operators. In particular, we obtain the normal ordering of a degenerate
integral power of the number operator multiplied by an integral power of the
creation boson operator in terms of boson operators where the degenerate
r-Stirling numbers of the second kind appear as the coefficients.
