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Friezes, weak friezes, and T-paths
- Source :
- Çanakçı, İ & Jørgensen, P 2021, ' Friezes, weak friezes, and T-paths ', Advances in Applied Mathematics, vol. 131, 102253 . https://doi.org/10.1016/j.aam.2021.102253, Advances in Applied Mathematics, 131:102253. Academic Press Inc.
- Publication Year :
- 2021
- Publisher :
- Academic Press Inc., 2021.
-
Abstract
- Frieze patterns form a nexus between algebra, combinatorics, and geometry. T-paths with respect to triangulations of surfaces have been used to obtain expansion formulae for cluster variables. This paper will introduce the concepts of weak friezes and T-paths with respect to dissections of polygons. Our main result is that weak friezes are characterised by satisfying an expansion formula which we call the T-path formula. We also show that weak friezes can be glued together, and that the resulting weak frieze is a frieze if and only if so was each of the weak friezes being glued.<br />17 pages
- Subjects :
- Cluster algebra
Polygon dissection
Frieze
Mathematics::Combinatorics
Applied Mathematics
010102 general mathematics
Frieze pattern
Positivity
01 natural sciences
05B45, 05E15, 05E99, 51M20
Combinatorics
Frieze group
0103 physical sciences
FOS: Mathematics
Mathematics - Combinatorics
Combinatorics (math.CO)
010307 mathematical physics
Generalised frieze pattern
0101 mathematics
Algebra over a field
Computer Science::Data Structures and Algorithms
Cluster expansion formula
Semifield
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 10902074 and 01968858
- Volume :
- 131
- Database :
- OpenAIRE
- Journal :
- Advances in Applied Mathematics
- Accession number :
- edsair.doi.dedup.....6251278b2b6f1630f83a9038a215ad16