A note on friezes of type ${\Lambda }_p$

Abstract

A frieze is an array of numbers obeying the unimodular rule. Coxeter showed that a frieze with integer entries corresponds to a triangulation. Recently, Holm and Jørgenson introduced friezes of type ${\Lambda }_p$ which correspond to $p$-angulations of a polygon. In this paper we explore the connection between these two types of friezes; in particular we show that the friezes of type ${\Lambda }_p$ for $p=4$ and $p=6$ contain integral friezes within them. We also consider the relationships with Farey graphs.

12 pages, 9 figures