A combinatorial model for tame frieze patterns

Let R be an arbitrary subset of a commutative ring. We introduce a combinatorial model for the set of tame frieze patterns with entries in R based on a notion of irreducibility of frieze patterns. When R is a ring, then a frieze pattern is reducible if and only if it contains an entry (not on the border) which is 1 or −1. To my knowledge, this model generalizes simultaneously all previously presented models for tame frieze patterns bounded by 0s and 1s