Corpus ID: 235422279

Periodic Infinite Frieze Patterns of Type $\Lambda_{p_1,\ldots,p_n}$ and Dissections on Annuli

@inproceedings{Banaian2021PeriodicIF,
  title={Periodic Infinite Frieze Patterns of Type \$\Lambda\_\{p\_1,\ldots,p\_n\}\$ and Dissections on Annuli},
  author={Esther Banaian and Jiuqi Chen},
  year={2021}
}
Finite frieze patterns with entries in Z[λp1 , . . . , λps ] where {p1, . . . , ps} ⊆ Z≥3 and λp = 2cos(π/p) were shown to have a connection to dissected polygons by Holm and Jørgensen. We extend their work by studying the connection between infinite frieze patterns with such entries and dissections of annuli and once-punctured discs. We give an algorithm to determine whether a frieze pattern with entries in Z[λp1 , . . . , λps ], finite or infinite, comes from a dissected surface. We introduce… Expand

Figures from this paper

References

SHOWING 1-10 OF 33 REFERENCES
Conway-Coxeter friezes and beyond: Polynomially weighted walks around dissected polygons and generalized frieze patterns
Conway and Coxeter introduced frieze patterns in 1973 and classified them via triangulated polygons. The determinant of the matrix associated to a frieze table was computed explicitly by Broline,Expand
Growth behaviour of periodic tame friezes
We examine the growth behaviour of the entries occurring in $n$-periodic tame friezes of real numbers. Extending \cite{T}, we prove that generalised recursive relations exist between all entries ofExpand
Arithmetic infinite friezes from punctured discs
We define the notion of infinite friezes of positive integers as a variation of Conway-Coxeter frieze patterns and study their properties. We introduce useful gluing and cutting operations onExpand
Cluster algebraic interpretation of infinite friezes
TLDR
By examining infinite friezes with Laurent polynomial entries, this paper discovers new symmetries and formulas relating the entries of this frieze to one another and presents a correspondence between Broline, Crowe and Isaacs’s classical matching tuples and combinatorial interpretations of elements of cluster algebras from surfaces. Expand
Friezes, weak friezes, and T-paths
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. ThisExpand
Infinite friezes and triangulations of annuli
It is known that any infinite frieze comes from a triangulation of an annulus by Baur, Parsons and Tschabold. In this paper we show that each periodic infinite frieze determines a triangulation of anExpand
A $p$-angulated generalisation of Conway and Coxeter's theorem on frieze patterns
Coxeter defined the notion of frieze pattern, and Conway and Coxeter proved that triangulations of polygons are in bijection with integral frieze patterns. We show a $p$-angulated generalisationExpand
The field Q(2cos(pi/n)), its Galois group and length ratios in the regular n-gon
The normal field extension Q(rho(n)), with the algebraic number rho(n) = 2 cos(pi/n) for natural n, is related to ratios of the lengths between diagonals and the side of a regular n-gon. This hasExpand
Lattice structure for orientations of graphs
Earlier researchers have studied the set of orientations of a connected finite graph $G$, and have shown that any two such orientations having the same flow-difference around all closed loops can beExpand
Infinite friezes
TLDR
This work provides a characterization of infinite frieze patterns of positive integers via triangulations of an infinite strip in the plane and gives a geometric interpretation of all entries of finite friezes via matching numbers. Expand
...
1
2
3
4
...