Subpolygons in Conway–Coxeter frieze patterns

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 ?

Linear Difference Equations, Frieze Patterns and Combinatorial Gale Transform

We study the space of linear di↵erence equations with periodic coe cients and (anti)periodic solutions. We show that this space is isomorphic to the space of tame frieze patterns and closely related to the moduli space of configurations of points in the projective space. We define the notion of combinatorial Gale transform which is a duality between periodic di↵erence equations of di↵erent orde...

Introducing Supersymmetric Frieze Patterns and Linear Difference Operators

We introduce a supersymmetric analog of the classical Coxeter frieze patterns. Our approach is based on the relation with linear difference operators. We define supersymmetric analogs of linear difference operators called Hill’s operators. The space of these “superfriezes” is an algebraic supervariety, which is isomorphic to the space of supersymmetric second order difference equations, called ...