The limiting distribution of the q-derangement numbers

Authors:
William Y. C. Chen;David G. L. Wang
Affiliations:
Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, PR China;Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, PR China
Venue:
European Journal of Combinatorics
Year:
2010

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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 limiting distribution of the coefficients of the usual q-derangement numbers of type B.