Vol. 14, No. 3, 2021

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

Julia E. Bergner, Cedric Harper, Ryan Keller and Mathilde Rosi-Marshall

Vol. 14 (2021), No. 3, 387–399
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 also give a comparison with planar rooted forests with a fixed number of trees.

Keywords
Catalan numbers, convolution of sequences, action graphs
Mathematical Subject Classification 2010
Primary: 05A19, 05C05
Milestones
Received: 18 February 2020
Revised: 15 October 2020
Accepted: 18 January 2021
Published: 17 July 2021

Communicated by Kenneth S. Berenhaut
Authors
Julia E. Bergner
Department of Mathematics
University of Virginia
Charlottesville, VA
United States
Cedric Harper
Department of Mathematics
University of Virginia
Charlottesville, VA
United States
Ryan Keller
Department of Mathematics
University of Virginia
Charlottesville, VA
United States
Mathilde Rosi-Marshall
Department of Mathematics
University of Virginia
Charlottesville, VA
United States