Details
| Original language | English |
|---|---|
| Article number | 102940 |
| Number of pages | 26 |
| Journal | Advances in Applied Mathematics |
| Volume | 171 |
| Early online date | 24 Jul 2025 |
| Publication status | Published - 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
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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In: Advances in Applied Mathematics, Vol. 171, 102940, 12.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Non-commutative friezes and their determinants, the non-commutative Laurent phenomenon for weak friezes, and frieze gluing
AU - Cuntz, Michael
AU - Holm, Thorsten
AU - Jørgensen, Peter
N1 - Publisher Copyright: © 2025 The Author(s)
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 - http://www.scopus.com/inward/record.url?scp=105011282280&partnerID=8YFLogxK
U2 - 10.1016/j.aam.2025.102940
DO - 10.1016/j.aam.2025.102940
M3 - Article
AN - SCOPUS:105011282280
VL - 171
JO - Advances in Applied Mathematics
JF - Advances in Applied Mathematics
SN - 0196-8858
M1 - 102940
ER -