Construction and Composition of Rooted Trees via Descent Functions
Marco Abrate, Stefano Barbero, Umberto Cerruti, Nadir Murru
TL;DR
This paper introduces descent functions as a new method for constructing and composing rooted trees, enabling the creation of rational and Pythagorean trees with novel properties.
Contribution
It presents a novel approach using descent functions for rooted tree construction and composition, leading to new types of rational and Pythagorean trees.
Findings
New method for constructing rooted trees
Ability to compose rooted trees systematically
Creation of rational and Pythagorean trees
Abstract
We propose a novel approach for studying rooted trees by using functions that we will call descent functions. We provide a construction method for rooted trees that allows to study their properties through the use of descent functions. Moreover, in this way, we are able to compose rooted trees with each other. Such a new composition of rooted trees is a very powerful tool applied in this paper in order to obtain important results as the creation of new rational and Pythagorean trees.
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Taxonomy
TopicsData Management and Algorithms · Polynomial and algebraic computation · Advanced Combinatorial Mathematics