Action graphs, planar rooted forests, and self-convolutions of the Catalan numbers

Abstract

We show that families of action graphs, with initial graphs which are linear of varying length, give rise to self-convolutions of the Catalan sequence. We prove this result via a comparison with planar rooted forests with a fixed number of trees.

arXiv comment11 pages; new proof added

References in corpus (2)

• Reedy categories which encode the notion of category actions
• Action graphs and Catalan numbers