Séminaire de l'Équipe Modèles Combinatoires - 2017

Mercredi 18 janvier
Emily Gunawan
(Gustavus Adolphus College)
Cluster algebraic interpretation of infinite friezes
Originally studied by Conway and Coxeter, friezes appeared in various recreational mathematics publications in the 1970s. More recently, in 2015, Baur, Parsons, and Tschabold constructed periodic infinite friezes and related them to matching numbers in the once-punctured disk and annulus. In this paper, we study such infinite friezes with an eye towards cluster algebras of type D and affine A, respectively. By examining infinite friezes with Laurent polynomials entries, we discover new symmetries and formulas relating the entries of this frieze to one another. Lastly, we also present a correspondence between Broline, Crowe and Isaacs’s classical matching tuples and combinatorial interpretations of elements of cluster algebras from surfaces.

Mercredi 26 avril 2017
Séance participative (Florent Hivert et Vincent Pilaud)

Mercredi 3 mai 2017
Séance participative

Mercredi 10 mai 2017
Mark Pankov
(University Warmia and Mazury)
Zigzags in embedded graphs and simplicial complexes
The concept of zigzag (Petrie polygon) was introduced by Coxeter and expanded by Deza. It is interesting for many reasons, for example, in context of projections of links. We consider z-knotted triangulations, i.e. triangulations with the unique zigzag, and describe all cases when the connected sum of z-knotted triangulations is z-knotted. Also, we discuss some relations of zigzags and distances between facets in simplicial complexes.