Infinite friezes and triangulations of annuli

Karin Baur; Ilke Çanakçl; Karin M. Jacobsen; Maitreyee C. Kulkarni; Gordana Todorov

doi:10.1142/S0219498824502074

Infinite friezes and triangulations of annuli

Karin Baur, Ilke Çanakçl, Karin M. Jacobsen, Maitreyee C. Kulkarni^*, Gordana Todorov

^*Corresponding author af dette arbejde

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Abstract

It is known that any infinite periodic frieze comes from a triangulation of an annulus by Theorem 4.6 of [K. Baur, M. J. Parsons and M. Tschabold, Infinite friezes, European J. Combin. 54 (2016) 220-237]. In this paper, we show that each infinite periodic frieze determines a triangulation of an annulus in essentially a unique way. Since each triangulation of an annulus determines a pair of friezes, we study such pairs and show how they determine each other. We study associated module categories and determine the growth coefficient of the pair of friezes in terms of modules as well as their quiddity sequences.

Originalsprog	Engelsk
Artikelnummer	2450207
Tidsskrift	Journal of Algebra and its Applications
Vol/bind	23
Nummer	12
ISSN	0219-4988
DOI	https://doi.org/10.1142/S0219498824502074
Status	Udgivet - okt. 2024

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title = "Infinite friezes and triangulations of annuli",

abstract = "It is known that any infinite periodic frieze comes from a triangulation of an annulus by Theorem 4.6 of [K. Baur, M. J. Parsons and M. Tschabold, Infinite friezes, European J. Combin. 54 (2016) 220-237]. In this paper, we show that each infinite periodic frieze determines a triangulation of an annulus in essentially a unique way. Since each triangulation of an annulus determines a pair of friezes, we study such pairs and show how they determine each other. We study associated module categories and determine the growth coefficient of the pair of friezes in terms of modules as well as their quiddity sequences.",

keywords = "annulus, cluster categories, Conway-Coxeter friezes, frieze patterns, growth coefficients, infinite friezes, triangulation",

author = "Karin Baur and Ilke {\c C}anak{\c c}l and Jacobsen, {Karin M.} and Kulkarni, {Maitreyee C.} and Gordana Todorov",

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doi = "10.1142/S0219498824502074",

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journal = "Journal of Algebra and its Applications",

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T1 - Infinite friezes and triangulations of annuli

AU - Baur, Karin

AU - Çanakçl, Ilke

AU - Jacobsen, Karin M.

AU - Kulkarni, Maitreyee C.

AU - Todorov, Gordana

PY - 2024/10

Y1 - 2024/10

N2 - It is known that any infinite periodic frieze comes from a triangulation of an annulus by Theorem 4.6 of [K. Baur, M. J. Parsons and M. Tschabold, Infinite friezes, European J. Combin. 54 (2016) 220-237]. In this paper, we show that each infinite periodic frieze determines a triangulation of an annulus in essentially a unique way. Since each triangulation of an annulus determines a pair of friezes, we study such pairs and show how they determine each other. We study associated module categories and determine the growth coefficient of the pair of friezes in terms of modules as well as their quiddity sequences.

AB - It is known that any infinite periodic frieze comes from a triangulation of an annulus by Theorem 4.6 of [K. Baur, M. J. Parsons and M. Tschabold, Infinite friezes, European J. Combin. 54 (2016) 220-237]. In this paper, we show that each infinite periodic frieze determines a triangulation of an annulus in essentially a unique way. Since each triangulation of an annulus determines a pair of friezes, we study such pairs and show how they determine each other. We study associated module categories and determine the growth coefficient of the pair of friezes in terms of modules as well as their quiddity sequences.

KW - annulus

KW - cluster categories

KW - Conway-Coxeter friezes

KW - frieze patterns

KW - growth coefficients

KW - infinite friezes

KW - triangulation

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DO - 10.1142/S0219498824502074

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SN - 0219-4988

VL - 23

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

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Infinite friezes and triangulations of annuli

Abstract

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