# Generalised friezes and the weak Ptolemy map

**Date**: Tuesday 19 March 2019, 16:00 – 17:00**Location**: Mathematics Level 8, MALL 1, School of Mathematics**Type**: Algebra, Seminars, Pure Mathematics**Cost**: PWYW

#### Ilke Canakci, University of Newcastle.

Frieze patterns, introduced by Conway, are infinite arrays of numbers where neighbouring numbers satisfy a local arithmetic rule. Frieze patterns with positive integer values are of a special interest since they are in one-to-one correspondence with triangulations of polygons by Conway--Coxeter. Remarkably, this established a connection to cluster algebras–predating them by 30 years– and to cluster categories. Several generalisations of frieze patterns are known. Joint with Jørgensen, we associated frieze patterns to dissections of polygons where the entries are over a (commutative) ring. Furthermore, we introduced an explicit combinatorial formula for the entries of these friezes by generalising the 'T-path formula' of Schiffler which was introduced to give explicit formulas for cluster variables for cluster algebras of type A.