Arithmetic Y-frieze patterns of width 3 and 4

TL;DR

This paper classifies all arithmetic Y-Frieze patterns of widths 3 and 4, establishing a link with Coxeter's Frieze patterns and confirming the surjectivity of a related map for these widths.

Contribution

It provides a complete classification of arithmetic Y-Frieze patterns for widths 3 and 4 and verifies the surjectivity of the map to Coxeter's Frieze patterns for these cases.

Findings

All arithmetic Y-Frieze patterns of width 3 and 4 are determined.

The surjectivity of the map p_n is verified for n=3,4.

Establishes a connection between Y-Frieze patterns and Coxeter's Frieze patterns.

Abstract

We determine all arithmetic Y-Frieze patterns of width $3$ and $4$. As a consequence, for $n=3,4$, we verify the surjectivity of a map $p_n$ which corresponds arithmetic Y-Frieze patterns of width $n$ to Coxeter's Frieze patterns.