Frieze patterns over algebraic numbers

Michael Cuntz; Thorsten Holm; Carlo Pagano

doi:10.48550/arXiv.2306.12148

Frieze patterns over algebraic numbers

Michael Cuntz
, Thorsten Holm
, Carlo Pagano

Institute of Algebra, Number Theory and Discrete Mathematics

Concordia University

Research output: Contribution to journal › Article › Research › peer review

Abstract

Conway and Coxeter have shown that frieze patterns over positive rational integers are in bijection with triangulations of polygons. An investigation of frieze patterns over other subsets of the complex numbers has recently been initiated by Jorgensen and the first two authors. In this paper we first show that a ring of algebraic numbers has finitely many units if and only if it is an order in a quadratic number field Q(\sqrt{d}) where d

Original language	English
Pages (from-to)	1417-1432
Number of pages	16
Journal	Bulletin of the London Mathematical Society
Volume	56
Issue number	4
DOIs	https://doi.org/10.48550/arXiv.2306.12148 https://doi.org/10.1112/blms.13003
Publication status	Published - 2 Apr 2024

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10.1112/blms.13003Licence: CC BY-NC-ND 4.0

Cite this

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abstract = "Conway and Coxeter have shown that frieze patterns over positive rational integers are in bijection with triangulations of polygons. An investigation of frieze patterns over other subsets of the complex numbers has recently been initiated by Jorgensen and the first two authors. In this paper we first show that a ring of algebraic numbers has finitely many units if and only if it is an order in a quadratic number field Q(\textbackslash{}sqrt\{d\}) where d",

author = "Michael Cuntz and Thorsten Holm and Carlo Pagano",

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AU - Pagano, Carlo

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N2 - Conway and Coxeter have shown that frieze patterns over positive rational integers are in bijection with triangulations of polygons. An investigation of frieze patterns over other subsets of the complex numbers has recently been initiated by Jorgensen and the first two authors. In this paper we first show that a ring of algebraic numbers has finitely many units if and only if it is an order in a quadratic number field Q(\sqrt{d}) where d

AB - Conway and Coxeter have shown that frieze patterns over positive rational integers are in bijection with triangulations of polygons. An investigation of frieze patterns over other subsets of the complex numbers has recently been initiated by Jorgensen and the first two authors. In this paper we first show that a ring of algebraic numbers has finitely many units if and only if it is an order in a quadratic number field Q(\sqrt{d}) where d

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Frieze patterns over algebraic numbers

Abstract

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