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A $p$-angulated generalisation of Conway and Coxeter's theorem on frieze patterns

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arxiv 1709.09861 v3 pith:RCRQ6JXB submitted 2017-09-28 math.CO

Thorsten Holm , Peter Jorgensen This is my paper · ORCID
classification math.CO
keywords friezepatternscoxeterangulatedconwaygeneralisationnon-integralbijection
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abstract

Coxeter defined the notion of frieze pattern, and Conway and Coxeter proved that triangulations of polygons are in bijection with integral frieze patterns. We show a $p$-angulated generalisation involving non-integral frieze patterns. We also show that polygon dissections give rise to even more general non-integral frieze patterns.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Frieze patterns with coefficients

    math.CO 2019-09 conditional novelty 7.0 of 10

    Tame frieze patterns with coefficients are developed, with a complete classification of triangles realizable from classic Conway-Coxeter friezes and a finiteness theorem over discrete subsets.

  2. On the construction of frieze patterns from partitions of convex polygons by nonintersecting diagonals

    math.CO 2025-09 conditional novelty 4.0 of 10

    An elementary proof that dissections of convex polygons into smaller polygons generate frieze patterns of width m-3.

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