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Categorification of a frieze pattern determinant

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arxiv 1008.5329 v2 pith:3JP5CMKF submitted 2010-08-31 math.CO math.RT

Karin Baur , Bethany Marsh This is my paper · ORCID
classification math.COmath.RT
keywords friezepatternclusterdeterminantresulttypealgebraarising
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Broline, Crowe and Isaacs have computed the determinant of a matrix associated to a Conway-Coxeter frieze pattern. We generalise their result to the corresponding frieze pattern of cluster variables arising from the Fomin-Zelevinsky cluster algebra of type A. We give a representation-theoretic interpretation of this result in terms of certain configurations of indecomposable objects in the root category of type A.

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  1. Frieze patterns and aperiodic tilings of the plane

    math.CO 2026-07 accept novelty 7.0 of 10

    Penrose rhombic tilings admit a four-valued vertex frieze pattern and Godrèche–Lançon–Billard tilings admit a three-valued one, both satisfying the diamond rule bc−ad=1.

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