A link between the generating function of skew domino tableaux and quasisymmetric functions of type B

In this paper, we consider the generating function of skew domino tableaux and conditions of decomposing it using fundamental quasisymmetric functions of type B. This question, as showed earlier by Mayorova and Vassilieva, is related to the descent statistics for elements of Coxeter groups and tableaux for Coxeter groups. In this paper, we obtain estimates of the number of diagrams that fit the conditions.