The Limiting Distribution of the q-Derangement Numbers
William Y.C. Chen and David G.L. Wang
Abstract: We prove the normality of the limiting distribution of the coefficients of the q-derangement numbers of type B based on the formula of Foata and Han that contains a parameter z. Setting the parameter z to zero, we are led to the case of ordinary q-derangement numbers. For z= 1, we obtain the normality of the distribution of the coefficients of the usual q-derangement numbers of type B.
AMS Classification: 05A15, 05A16
Keywords: limiting distribution, q-derangement number, flag major index, moment generating function