A proof of Catalan's Convolution formula

2011/09/02 by Alon Regev, Regev, Alon
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1109.0571

arxiv created 2011/09/02 · arxiv updated 2011/09/06

Abstract

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.

Related

• Convolution numbers: the cyclic case
• Alternating Convolutions of Catalan Numbers
• The Location of the First Ascent in a 123-Avoiding Permutation
• Multifold Convolutions, Generating Functions and 1d Random Walks
• A variant of Touchard's Catalan number identity