Infinite friezes
Karin Baur, Mark James Parsons, Manuela Tschabold
TL;DR
This paper characterizes infinite frieze patterns of positive integers using triangulations of an infinite strip, offering geometric interpretations and connections to annuli in the periodic case.
Contribution
It introduces a novel geometric framework for understanding infinite friezes through triangulations and matching numbers, extending previous finite frieze theories.
Findings
Characterization of infinite friezes via triangulations
Geometric interpretation of frieze entries as matching numbers
Extension of finite frieze concepts to infinite cases
Abstract
We provide a characterization of infinite frieze patterns of positive integers via triangulations of an infinite strip in the plane. In the periodic case, these triangulations may be considered as triangulations of annuli. We also give a geometric interpretation of all entries of infinite friezes via matching numbers.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology · Geometric Analysis and Curvature Flows