Solutions monomiales minimales irr\'eductibles dans $SL_{2}(\mathbb{Z}/p^{n}\mathbb{Z})$

Flavien Mabilat

Solutions monomiales minimales irr\'eductibles dans $SL_{2}(\mathbb{Z}/p^{n}\mathbb{Z})$

Combinatorics 2023-09-07 v2

Authors: Flavien Mabilat

Abstract

In this article, we study the combinatorics of congruence subgroups of the modular group. More precisely, we consider the notion of minimal monomial solutions. These are the solutions of a matrix equation (also appearing in the study of Coxeter friezes), modulo an integer $N$ , whose components are identical and minimal for this property. The objective here is to characterize the solutions of this type verifying a property of irreducibility modulo a prime power.

Keywords

congruence subgroups modular group minimal monomial solutions matrix equation irreducibility prime power combinatorics

Cite

@article{arxiv.2202.07279,
  title  = {Solutions monomiales minimales irr\'eductibles dans $SL_{2}(\mathbb{Z}/p^{n}\mathbb{Z})$},
  author = {Flavien Mabilat},
  journal= {arXiv preprint arXiv:2202.07279},
  year   = {2023}
}

Comments

in French language \`a para\^itre dans le Bulletin des Sciences Math\'ematiques. arXiv admin note: text overlap with arXiv:2112.10410, arXiv:2105.11719

Solutions monomiales minimales irr\'eductibles dans $SL_{2}(\mathbb{Z}/p^{n}\mathbb{Z})$

Abstract

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