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

Michael Cuntz; Thorsten Holm; Peter Jørgensen

doi:10.1016/j.aam.2025.102940

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

Michael Cuntz
, Thorsten Holm
, Peter Jørgensen

Institute of Algebra, Number Theory and Discrete Mathematics

Aarhus University

Research output: Contribution to journal › Article › Research › peer review

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.

Original language	English
Article number	102940
Number of pages	26
Journal	Advances in Applied Mathematics
Volume	171
E-pub ahead of print	24 Jul 2025
DOIs	https://doi.org/10.1016/j.aam.2025.102940 https://doi.org/10.48550/arXiv.2410.13507
Publication status	Published - Dec 2025

Keywords

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

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aam.2025.102940Licence: CC BY 4.0
10.48550/arXiv.2410.13507Licence: Arxiv nonexclusive-distrib 1.0

Cite this

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

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 {\c C}anak{\c c}ı and J{\o}rgensen.",

keywords = "Cluster algebra, Cluster expansion formula, Coxeter frieze, Dieudonn{\'e} determinant, Generalised frieze, Polygon dissection, Skew field, T-path formula, Weak frieze",

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AU - Cuntz, Michael

AU - Holm, Thorsten

AU - Jørgensen, Peter

PY - 2025/12

Y1 - 2025/12

N2 - 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.

AB - 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.

KW - Cluster algebra

KW - Cluster expansion formula

KW - Coxeter frieze

KW - Dieudonné determinant

KW - Generalised frieze

KW - Polygon dissection

KW - Skew field

KW - T-path formula

KW - Weak frieze

UR - https://www.scopus.com/pages/publications/105011282280

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DO - 10.1016/j.aam.2025.102940

M3 - Article

AN - SCOPUS:105011282280

SN - 0196-8858

VL - 171

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

M1 - 102940

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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