On upper bounds of frieze patterns

TL;DR

This paper establishes that the maximum values in frieze patterns of types A_n and C_n follow Fibonacci and odd Fibonacci sequences respectively, revealing a deep combinatorial connection.

Contribution

It identifies the exact sequences governing maximum values in frieze patterns of types A_n and C_n, linking them to Fibonacci numbers.

Findings

Maximum values in A_n frieze patterns are Fibonacci numbers.

Maximum values in C_n frieze patterns are odd Fibonacci numbers.

The sequences follow a precise mathematical pattern.

Abstract

In this note, we show that the sequence of maximum values in frieze patterns of type $A_n$ is the sequence of Fibonacci numbers, and that of frieze patterns of type $C_n$ is the sequence of odd Fibonacci numbers.