Étude de quelques familles de $λ$-quiddités et minoration de la taille maximale des $λ$-quiddités irréductibles sur un corps fini

$λ$-quiddities of size $n$ are $n$-tuples of elements from a fixed set that are solutions to a matrix equation which is fundamental in the study of the combinatorics of the modular group and Coxeter's friezes. To gain further insight into these objects, we use a notion of irreducibility, which allow