Experimental Number Theory, Part I : Tower Arithmetic

TL;DR

This paper introduces a novel algebraic and combinatorial framework for number theory by representing numbers as rooted trees, called towers, revealing unexpected links between number theory, combinatorics, and probability.

Contribution

It presents a new approach that models numbers as combinatorial objects, providing fresh insights into their structure and connections to other mathematical fields.

Findings

Numbers are represented as rooted trees (towers).

The approach uncovers unexpected links between number theory, combinatorics, and probability.

Provides a new perspective on number theory through combinatorial objects.

Abstract

We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here refer to as towers. The bijection between numbers and towers provides some insights into unexpected connexions between Number theory, combinatorics and discrete probability theory.