Infinite friezes and triangulations of annuli
نویسندگان
چکیده
It is known that any infinite periodic frieze comes from a triangulation of an annulus by Theorem 4.6 [K. Baur, M. J. Parsons and Tschabold, Infinite friezes, European Combin. 54 (2016) 220–237]. In this paper, we show each determines in essentially unique way. Since pair study such pairs how they determine other. We associated module categories the growth coefficient friezes terms modules as well their quiddity sequences.
منابع مشابه
Sl2(z)-tilings of the Torus, Coxeter-conway Friezes and Farey Triangulations
The notion of SL2-tiling is a generalization of that of classical Coxeter-Conway frieze pattern. We classify doubly antiperiodic SL2-tilings that contain a rectangular domain of positive integers. Every such SL2-tiling corresponds to a pair of frieze patterns and a unimodular 2 × 2-matrix with positive integer coefficients. We relate this notion to triangulated n-gons in the Farey graph.
متن کاملAn infinite family of tight triangulations of manifolds
We give explicit construction of vertex-transitive tight triangulations of d-manifolds for d ≥ 2. More explicitly, for each d ≥ 2, we construct two (d + 5d + 5)-vertex neighborly triangulated d-manifolds whose vertex-links are stacked spheres. The only other non-trivial series of such tight triangulated manifolds currently known is the series of non-simply connected triangulated d-manifolds wit...
متن کاملImperfect friezes of integers
We show that for any positive forward density subset N ⊂ Z, there exists N ∈ N , such that, for all n ≥ N , N contains almost perfect n-scaled reproductions of any previously chosen finite set of integers.
متن کاملArithmetics of 2-friezes
We consider the variant of Coxeter–Conway frieze patterns called 2-frieze. We prove that there exist infinitely many closed integral 2-friezes (i.e. containing only positive integers) provided the width of the array is bigger than 4. We introduce operations on the integral 2-friezes generating bigger or smaller closed integral 2friezes.
متن کاملMinimal triangulations for an infinite family of lens spaces
The notion of a layered triangulation of a lens space was defined by Jaco and Rubinstein in [6], and, unless the lens space is L(3,1), a layered triangulation with the minimal number of tetrahedra was shown to be unique and termed its minimal layered triangulation. This paper proves that for each n ≥ 2, the minimal layered triangulation of the lens space L(2n,1) is its unique minimal triangulat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2023
ISSN: ['1793-6829', '0219-4988']
DOI: https://doi.org/10.1142/s0219498824502074