F. Mabilat

activity

20192026

collaborators

9 papers

math.RA2026

Decomposition of a square matrix into a product of a nilpotent matrix and an involutive or idempotent matrix

Flavien Mabilat

In this note, we give a complete characterization of square matrices of size $n$ over a commutative field which can be expressed as a product of a nilpotent matrix and an involutiv…

math.RA2026

Product of two matrices similar to companion matrices over sufficiently large fields

Flavien Mabilat

In this note, we prove that a square matrix of size $n$ over a field containing at least $2 n$ elements can be expressed as the product of two matrices similar to companion matrices…

math.CO2026

Maximal size of irreducible $λ$ -quiddities over polynomial and formal power series rings

Flavien Mabilat

The study of the combinatorics of the modular group and of Coxeter's friezes naturally leads to the investigation of a matrix equation, sometimes referred to as the Conway-Coxeter…

math.CO2024

Number of roots of the continuant over a finite local ring

Flavien Mabilat

The aim of this article is to obtain a formula giving, for a positive integer $n$ , the number of roots of the $n^{t h}$ continuant polynomial over a finite local ring. In particular…

math.CO2024

Finiteness of the number of irreducible $λ$ -quiddities over a finite commutative and unitary ring

Flavien Mabilat

A $λ$ -quiddity of size $n$ is an $n$ -tuple of elements from a fixed set, which is a solution to a matrix equation that arises in the study of Coxeter's friezes. The study of these…

math.CO2024

Some counting formulas for $λ$ -quiddities over the rings $Z / 2^{m} Z$

Flavien Mabilat

The $λ$ -quiddities of size $n$ are $n$ -tuples of elements of a fixed set, solutions of a matrix equation appearing in the study of Coxeter's friezes. Their number and their propert…

math.RA2023

A dense subset of $M_n (R)$ containing diagonalizable matrices

Flavien Mabilat

In this note, we consider matrices similar to $X$ -form matrices, which are the matrices for which only the diagonal and the anti-diagonal elements can be different from zero. First…

math.CO2022

$λ$ -quiddity and subgroups generated by an algebraic number

Flavien Mabilat

During his work devoted to Coxeter's friezes, M. Cuntz initiated the study of the notion of $λ$ -quiddity and raised the problem of the study of this over some subsets of $\mathbb C…

math.CO2019

Combinatorial description of the principal congruence subgroup $γ$ (2) in SL(2, z)

Flavien Mabilat

We characterize sequences of positive integers (c 1 , c 2 , ..., cn) for which the (2 x 2)-matrix c 1 --1 1 0 $\times$ $\times$ $\times$ cn --1 1 0 belongs to the principal congrue…

Decomposition of a square matrix into a product of a nilpotent matrix and an involutive or idempotent matrix

Product of two matrices similar to companion matrices over sufficiently large fields

Maximal size of irreducible λ-quiddities over polynomial and formal power series rings

Number of roots of the continuant over a finite local ring

Finiteness of the number of irreducible λ-quiddities over a finite commutative and unitary ring

Some counting formulas for λ-quiddities over the rings Z/2mZ

A dense subset of M_n(R) containing diagonalizable matrices

λ-quiddity and subgroups generated by an algebraic number

Combinatorial description of the principal congruence subgroup γ(2) in SL(2, z)

Maximal size of irreducible $λ$ -quiddities over polynomial and formal power series rings

Finiteness of the number of irreducible $λ$ -quiddities over a finite commutative and unitary ring

Some counting formulas for $λ$ -quiddities over the rings $Z / 2^{m} Z$

A dense subset of $M_n (R)$ containing diagonalizable matrices

$λ$ -quiddity and subgroups generated by an algebraic number

Combinatorial description of the principal congruence subgroup $γ$ (2) in SL(2, z)