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

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