Frieze patterns:
> Frieze patterns were introduced and studied by Coxeter and then Conway-Coxeter in the 70's. They are arrays of a
> finite number of shifted infinite rows of positive integers, satisfying the unimodular rule: in each square formed by four entries,
> the product of the horizontal entries is one more than the product of the vertical entries. An example is here:
>
> 0 0 0 0 0 0 0 0 0 0
> 1 1 1 1 1 1 1 1 1
> 2 1 3 1 2 2 1 3 1 2
> 1 2 2 1 3 1 2 2 1
> 1 1 1 1 1 1 1 1 1
> 0 0 0 0 0 0 0 0 0
>
> Conway-Coxeter have shown that such patterns are invariant under a glide symmetry and hence are peridoci. Furthermore,
> they are characterized by triangulations of polygons. We will briefly recall this and then consider infinite frieze patterns
> of positive integers. We show that they are also characterized by triangulations of surfaces. As in the finite case, we are
> able to give a geometric interpretation of all entries of an infinite frieze via matching numbers. This is joint work with M.J. Parsons
> and M. Tschabold (both from Graz).