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

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

2007-08-20

arxiv.org/abs/0708.2574v1

Mathematics

Combinatorics

13 pages

Scientific paper

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.

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