Subpolygons in Conway-Coxeter frieze patterns

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OriginalspracheEnglisch
Seiten (von - bis)741-755
Seitenumfang15
FachzeitschriftAlgebraic Combinatorics
Jahrgang4
Ausgabenummer4
PublikationsstatusVeröffentlicht - 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.

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Subpolygons in Conway-Coxeter frieze patterns. / Cuntz, Michael; Holm, Thorsten.
in: Algebraic Combinatorics, Jahrgang 4, Nr. 4, 02.09.2021, S. 741-755.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Cuntz M, Holm T. Subpolygons in Conway-Coxeter frieze patterns. Algebraic Combinatorics. 2021 Sep 2;4(4):741-755. doi: 10.5802/ALCO.180
Cuntz, Michael ; Holm, Thorsten. / Subpolygons in Conway-Coxeter frieze patterns. in: Algebraic Combinatorics. 2021 ; Jahrgang 4, Nr. 4. S. 741-755.
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