Non-commutative friezes and their determinants, the non-commutative Laurent phenomenon for weak friezes, and frieze gluing

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Original languageEnglish
Article number102940
Number of pages26
JournalAdvances in Applied Mathematics
Volume171
Early online date24 Jul 2025
Publication statusPublished - Dec 2025

Abstract

This paper studies a non-commutative generalisation of Coxeter friezes due to Berenstein and Retakh. It generalises several earlier results to this situation: A formula for frieze determinants, a T-path formula expressing the Laurent phenomenon, and results on gluing friezes together. One of our tools is a non-commutative version of the weak friezes introduced by Çanakçı and Jørgensen.

Keywords

    Cluster algebra, Cluster expansion formula, Coxeter frieze, Dieudonné determinant, Generalised frieze, Polygon dissection, Skew field, T-path formula, Weak frieze

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Non-commutative friezes and their determinants, the non-commutative Laurent phenomenon for weak friezes, and frieze gluing. / Cuntz, Michael; Holm, Thorsten; Jørgensen, Peter.
In: Advances in Applied Mathematics, Vol. 171, 102940, 12.2025.

Research output: Contribution to journalArticleResearchpeer review

Cuntz M, Holm T, Jørgensen P. Non-commutative friezes and their determinants, the non-commutative Laurent phenomenon for weak friezes, and frieze gluing. Advances in Applied Mathematics. 2025 Dec;171:102940. Epub 2025 Jul 24. doi: 10.1016/j.aam.2025.102940, 10.48550/arXiv.2410.13507
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