Full binary trees, Narayana numbers and two-dimensional decompositions of integers

TL;DR

This paper explores the connections between full binary trees, Narayana numbers, and integer decompositions, introducing two multitype Galton-Watson tree models and analyzing their statistical properties.

Contribution

It introduces two novel models of multitype Galton-Watson trees linked to Narayana numbers and integer decompositions, with detailed statistical analysis.

Findings

Relations between full binary trees and Narayana numbers established

Statistical properties of contour processes analyzed

Offspring distributions characterized

Abstract

We present two models of multitype Galton-Watson trees, that we call full binary trees and full binary trees with survivals. We show relevant relations between these trees and the Narayana numbers and the two-dimensional decompositions of integers. We prove further statistical results on our models concerning the related contour processes and offspring distributions.