Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 741-755 |
| Seitenumfang | 15 |
| Fachzeitschrift | Algebraic Combinatorics |
| Jahrgang | 4 |
| Ausgabenummer | 4 |
| Publikationsstatus | Veröffentlicht - 2 Sept. 2021 |
Abstract
Friezes with coefficients are maps assigning numbers to the edges and diagonals of a regular polygon such that all Ptolemy relations for crossing diagonals are satisfied. Among these, the classic Conway-Coxeter friezes are the ones where all values are positive integers and all edges have value 1. Every subpolygon of a Conway-Coxeter frieze yields a frieze with coefficients over the positive integers. In this paper we give a complete arithmetic criterion for which friezes with coefficients appear as subpolygons of Conway-Coxeter friezes. This generalizes a result of our earlier paper with Peter Jørgensen from triangles to subpolygons of arbitrary size.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Diskrete Mathematik und Kombinatorik
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in: Algebraic Combinatorics, Jahrgang 4, Nr. 4, 02.09.2021, S. 741-755.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Subpolygons in Conway-Coxeter frieze patterns
AU - Cuntz, Michael
AU - Holm, Thorsten
PY - 2021/9/2
Y1 - 2021/9/2
N2 - Friezes with coefficients are maps assigning numbers to the edges and diagonals of a regular polygon such that all Ptolemy relations for crossing diagonals are satisfied. Among these, the classic Conway-Coxeter friezes are the ones where all values are positive integers and all edges have value 1. Every subpolygon of a Conway-Coxeter frieze yields a frieze with coefficients over the positive integers. In this paper we give a complete arithmetic criterion for which friezes with coefficients appear as subpolygons of Conway-Coxeter friezes. This generalizes a result of our earlier paper with Peter Jørgensen from triangles to subpolygons of arbitrary size.
AB - Friezes with coefficients are maps assigning numbers to the edges and diagonals of a regular polygon such that all Ptolemy relations for crossing diagonals are satisfied. Among these, the classic Conway-Coxeter friezes are the ones where all values are positive integers and all edges have value 1. Every subpolygon of a Conway-Coxeter frieze yields a frieze with coefficients over the positive integers. In this paper we give a complete arithmetic criterion for which friezes with coefficients appear as subpolygons of Conway-Coxeter friezes. This generalizes a result of our earlier paper with Peter Jørgensen from triangles to subpolygons of arbitrary size.
KW - Cluster algebra
KW - Frieze pattern
KW - Polygon
KW - Quiddity cycle
KW - Tame frieze pattern
KW - Triangulation
UR - http://www.scopus.com/inward/record.url?scp=85115260766&partnerID=8YFLogxK
U2 - 10.5802/ALCO.180
DO - 10.5802/ALCO.180
M3 - Article
AN - SCOPUS:85115260766
VL - 4
SP - 741
EP - 755
JO - Algebraic Combinatorics
JF - Algebraic Combinatorics
IS - 4
ER -