Details
| Original language | English |
|---|---|
| Pages (from-to) | 741-755 |
| Number of pages | 15 |
| Journal | Algebraic Combinatorics |
| Volume | 4 |
| Issue number | 4 |
| Publication status | Published - 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.
Keywords
- Cluster algebra, Frieze pattern, Polygon, Quiddity cycle, Tame frieze pattern, Triangulation
ASJC Scopus subject areas
- Mathematics(all)
- Discrete Mathematics and Combinatorics
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In: Algebraic Combinatorics, Vol. 4, No. 4, 02.09.2021, p. 741-755.
Research output: Contribution to journal › Article › Research › 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 -