Frieze patterns over finite commutative local rings

Abstract

We count numbers of tame frieze patterns with entries in a finite commutative local ring. For the ring $\mathbb{Z}/p^r\mathbb{Z}$, $p$ a prime and $r\in \mathbb{N}$ we obtain closed formulae for all heights. These may be interpreted as formulae for the numbers of certain relations in quotients of the modular group.

fixed a typo in the case $p=2$ in Theorem 1.2