The Limiting Distribution of the Coefficients of the $q$-Catalan Numbers

Chen, William Y. C.; Wang, Carol J.; Wang, Larry X. W.

The Limiting Distribution of the Coefficients of the $q$-Catalan Numbers

Authors

Chen, William Y. C.

Wang, Carol J.

Wang, Larry X. W.

Description

We show that the limiting distributions of the coefficients of the $q$-Catalan numbers and the generalized $q$-Catalan numbers are normal. Despite the fact that these coefficients are not unimodal for small $n$, we conjecture that for sufficiently large $n$, the coefficients are unimodal and even log-concave except for a few terms of the head and tail.
13 pages