Frieze Patterns of Integers

Gait Sequence Analysis Using Frieze Patterns

We analyze walking people using a gait sequence representation that bypasses the need for frame-to-frame tracking of body parts. The gait representation maps a video sequence of silhouettes into a pair of two-dimensional spatio-temporal patterns that are periodic along the time axis. Mathematically, such patterns are called “frieze” patterns and associated symmetry groups “frieze groups”. With ...

Frieze patterns for punctured discs

We construct frieze patterns of type DN with entries which are numbers of matchings between vertices and triangles of corresponding triangulations of a punctured disc. For triangulations corresponding to orientations of the Dynkin diagram of type DN , we show that the numbers in the pattern can be interpreted as specialisations of cluster variables in the corresponding Fomin-Zelevinsky cluster ...

Gait Sequen e Analysis using Frieze Patterns ?

Coxeter’s Frieze Patterns and Discretization of the Virasoro Orbit

We show that the space of classical Coxeter’s frieze patterns can be viewed as a discrete version of a coadjoint orbit of the Virasoro algebra. The canonical (cluster) (pre)symplectic form on the space of frieze patterns is a discretization of the Kirillov symplectic form. We relate a continuous version of frieze patterns to conformal metrics of constant curvature in dimension 2.

The combinatorics of frieze patterns and Markoff numbers

This article, based on joint work with Gabriel Carroll, Andy Itsara, Ian Le, Gregg Musiker, Gregory Price, Dylan Thurston, and Rui Viana, presents a combinatorial model based on perfect matchings that explains the symmetries of the numerical arrays that Conway and Coxeter dubbed frieze patterns. This matchings model is a combinatorial interpretation of Fomin and Zelevinsky’s cluster algebras of...