"M" arc diagrams and their relationship to Borel's triangle
Abstract
The Catalan Numbers famously count many combinatorial sets including arc diagrams on 2n points and binary trees on n vertices. In this paper, I show that there is a bijection between extended leaf marked binary trees on n unmarked vertices and k marked vertices and "m" arc diagrams on 2n-k points by creating two functions that map between extended leaf marked binary trees and "m" arc diagrams. I then show that these functions are inverse bijections.