All Y-friezes come from SL_2-friezes

par Andrei Zabolotskii (Open Univ.)

vendredi 4 sept. 2026, 11:30 → 12:30 Europe/Paris

Amphi Jordan (Bat. Braconnier)

Y-friezes are "shadows" of Y-cluster variables, like Conway–Coxeter friezes are "shadows" of cluster variables. We resolve a conjecture of de Saint Germain, showing that all Y-friezes arise from Conway–Coxeter friezes. We give a threefold characterisation of those Conway–Coxeter friezes that give rise to the same Y-frieze: an elementary characterisation using quiddities, a combinatorial characterisation using triangulated polygons, and a geometrical characterisation using chains of horocycles.