A note on friezes of type $\Lambda_p$

TL;DR

This paper explores friezes of type Λ_p, connecting them to triangulations and p-angulations, and shows that certain friezes contain integral friezes, also examining their relation to Farey graphs.

Contribution

It establishes the connection between friezes of type Λ_p and geometric structures like triangulations and p-angulations, highlighting integral friezes within these types.

Findings

Friezes of type Λ_4 and Λ_6 contain integral friezes.

Connections between Λ_p friezes and Farey graphs are explored.

The relationship between friezes and geometric structures is clarified.

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 J{\o}rgenson 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.