Arithmetics of 2-friezes

We consider the variant of Coxeter–Conway frieze patterns called 2-frieze. We prove that there exist infinitely many closed integral 2-friezes (i.e. containing only positive integers) provided the width of the array is bigger than 4. We introduce operations on the integral 2-friezes generating bigge...

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Bibliographic Details
Published in:Journal of algebraic combinatorics 2012-12, Vol.36 (4), p.515-539
Main Author: Morier-Genoud, Sophie
Format: Article
Language:English
Subjects:
Combinatorics
Computer Science
Convex and Discrete Geometry
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
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Summary:We consider the variant of Coxeter–Conway frieze patterns called 2-frieze. We prove that there exist infinitely many closed integral 2-friezes (i.e. containing only positive integers) provided the width of the array is bigger than 4. We introduce operations on the integral 2-friezes generating bigger or smaller closed integral 2-friezes.
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-012-0348-2