A combinatorial model for tame frieze patterns

2017/11/27 by Michael Cuntz, Cuntz, Michael · 2 citations
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Artificial Intelligence in Games #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1711.09687

Abstract

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 0's and 1's.

Cited by

• Combinatorial description of the principal congruence subgroup\n \γ(2) in SL(2, z)
• Factorization of Frieze Patterns

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