6 papers
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 over a commutative field which can be expressed as a product of a nilpotent matrix and an involutiv…
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 , the number of roots of the continuant polynomial over a finite local ring. In particular…
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 over a field containing at least elements can be expressed as the product of two matrices similar to companion matrices…
Maximal size of irreducible -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…
-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 -quiddity and raised the problem of the study of this over some subsets of $\mathbb…
Finiteness of the number of irreducible -quiddities over a finite commutative and unitary ring
Flavien Mabilat
A -quiddity of size is an -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…