Arithmetics of 2-friezes

TL;DR

This paper studies 2-frieze patterns, proving the existence of infinitely many positive integer solutions for arrays wider than 4, and introduces operations to generate larger or smaller integral 2-friezes.

Contribution

It establishes the infinite existence of closed integral 2-friezes for widths greater than 4 and introduces operations to manipulate these friezes.

Findings

Infinitely many closed integral 2-friezes exist for width > 4

Operations can generate larger or smaller integral 2-friezes

Positive integer solutions are abundant for wider arrays

Abstract

We consider the variant of Coxeter-Conway frieze patterns called 2-frieze. We prove that there exist infinitely many closed integral 2-friezes (i.e. containing only positive integers) provided the width of the array is bigger than 4. We introduce operations on the integral 2-friezes generating bigger or smaller closed integral 2-friezes.