Combinatoire des Sous-Groupes de Congruence du Groupe Modulaire II

TL;DR

This paper explores the combinatorics of congruence subgroups of the modular group, focusing on matrix equations related to Coxeter friezes, and introduces new concepts like minimal dynomial solutions.

Contribution

It provides new properties of minimal monomial solutions and introduces the notion of minimal dynomial solutions, advancing the understanding of their irreducibility.

Findings

New properties for minimal monomial solutions

Introduction of minimal dynomial solutions

Analysis of irreducibility in solutions

Abstract

In this paper, we study combinatorics of congruence subgroups of the modular group. More precisely, we consider the matrix equation that naturally arises in the theory of Coxeter friezes and investigate its irreducible solutions. We give new properties for minimal monomial solutions. Furthermore, we introduce the notion of minimal dynomial solutions and study their irreducibility.