Find

Institut for Matematik

Friezes, weak friezes, and T-paths

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

Standard

Friezes, weak friezes, and T-paths. / Çanakçı, İlke; Jørgensen, Peter.

I: Advances in Applied Mathematics, Bind 131, 102253, 10.2021.

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

Vancouver

Çanakçı İ, Jørgensen P. Friezes, weak friezes, and T-paths. Advances in Applied Mathematics. 2021 okt.;131:102253. doi: 10.1016/j.aam.2021.102253

Author

Çanakçı, İlke ; Jørgensen, Peter. / Friezes, weak friezes, and T-paths. I: Advances in Applied Mathematics. 2021 ; Bind 131.

Bibtex

@article{15403b9e278f4f6a82f8468b006f4dac,

title = "Friezes, weak friezes, and T-paths",

abstract = "Frieze patterns form a nexus between algebra, combinatorics, and geometry. T-paths with respect to triangulations of surfaces have been used to obtain expansion formulae for cluster variables. This paper will introduce the concepts of weak friezes and T-paths with respect to dissections of polygons. Our main result is that weak friezes are characterised by satisfying an expansion formula which we call the T-path formula. We also show that weak friezes can be glued together, and that the resulting weak frieze is a frieze if and only if so was each of the weak friezes being glued.",

keywords = "Cluster algebra, Cluster expansion formula, Frieze pattern, Generalised frieze pattern, Polygon dissection, Positivity, Semifield",

author = "İlke {\c C}anak{\c c}ı and Peter J{\o}rgensen",

note = "Publisher Copyright: {\textcopyright} 2021 The Authors",

year = "2021",

month = oct,

doi = "10.1016/j.aam.2021.102253",

language = "English",

volume = "131",

journal = "Advances in Applied Mathematics",

issn = "0196-8858",

publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Friezes, weak friezes, and T-paths

AU - Çanakçı, İlke

AU - Jørgensen, Peter

PY - 2021/10

Y1 - 2021/10

N2 - Frieze patterns form a nexus between algebra, combinatorics, and geometry. T-paths with respect to triangulations of surfaces have been used to obtain expansion formulae for cluster variables. This paper will introduce the concepts of weak friezes and T-paths with respect to dissections of polygons. Our main result is that weak friezes are characterised by satisfying an expansion formula which we call the T-path formula. We also show that weak friezes can be glued together, and that the resulting weak frieze is a frieze if and only if so was each of the weak friezes being glued.

AB - Frieze patterns form a nexus between algebra, combinatorics, and geometry. T-paths with respect to triangulations of surfaces have been used to obtain expansion formulae for cluster variables. This paper will introduce the concepts of weak friezes and T-paths with respect to dissections of polygons. Our main result is that weak friezes are characterised by satisfying an expansion formula which we call the T-path formula. We also show that weak friezes can be glued together, and that the resulting weak frieze is a frieze if and only if so was each of the weak friezes being glued.

KW - Cluster algebra

KW - Cluster expansion formula

KW - Frieze pattern

KW - Generalised frieze pattern

KW - Polygon dissection

KW - Positivity

KW - Semifield

UR - http://www.scopus.com/inward/record.url?scp=85111068692&partnerID=8YFLogxK

U2 - 10.1016/j.aam.2021.102253

DO - 10.1016/j.aam.2021.102253

M3 - Journal article

AN - SCOPUS:85111068692

VL - 131

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

SN - 0196-8858

M1 - 102253

ER -