A proof of Catalan's Convolution formula

Details A proof of Catalan's Convolution formula A proof of Catalan's Convolution formula

2011-09-02

arxiv.org/abs/1109.0571v1

Mathematics

Combinatorics

Scientific paper

We give a new proof of the $k$-fold convolution of the Catalan numbers. This
is done by enumerating a certain class of polygonal dissections called
$k$-in-$n$ dissections. Furthermore, we give a formula for the average number
of cycles in a triangulation.

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