A q, r-analogue for the Stirling numbers of the second kind of Coxeter groups of type B

A generalization of the Stirling numbers of the second kind of type is given in two different directions. One generalization is via their -analogue and the other one uses distinguished elements. Both directions are explained and proved in a combinatorial way using generalized restricted growth words which we define here for type . Moreover, we present their ordinary and exponential generating functions, where the exponential generating function is also used to present the -variant as connection constants between two bases of ℝ[ ].