The combinatorics of frieze patterns and Markoff numbers

James Propp

Type: Preprint

Publication Date: 2005-01-01

Citations: 96

DOI: https://doi.org/10.48550/arxiv.math/0511633

View Publication

Locations

arXiv (Cornell University) - View
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	The combinatorics of frieze patterns and Markoff numbers	2006	James Propp
+	Frieze patterns and Farey complexes	2023	Ian Short Matty van Son Andrei Zabolotskii
+ PDF Chat	Cluster algebraic interpretation of infinite friezes	2019	Emily Gunawan Gregg Musiker Hannah Vogel
+ PDF Chat	Coxeter's frieze patterns at the crossroads of algebra, geometry and combinatorics	2015	Sophie Morier-Genoud
+ PDF Chat	FRIEZE PATTERNS WITH COEFFICIENTS	2020	Michael Cuntz Thorsten Holm Peter Jørgensen
+	Heronian friezes	2019	Sergey Fomin Linus Setiabrata
+	Frieze patterns over integers and other subsets of the complex numbers	2017	Michael Cuntz Thorsten Holm
+ PDF Chat	Frieze patterns over integers and other subsets of the complex numbers	2019	Michael Cuntz Thorsten Holm
+	Frieze patterns over integers and other subsets of the complex numbers.	2017	Michael Cuntz Thorsten Holm
+ PDF Chat	Perfect Matchings and Cluster Algebras of Classical Type	2008	Gregg Musiker
+	Frieze patterns of integers	2021	Karin Baur
+ PDF Chat	Frieze Patterns of Integers	2021	Karin Baur
+	Frieze patterns of integers	2021	Karin Baur
+	Friezes and continuant polynomials with parameters	2014	Véronique Bazier‐Matte David Racicot-Desloges Tanna Sanchez
+	Friezes of cluster algebras of geometric type	2023	Antoine de Saint Germain Min Huang Jiang-Hua Lu
+	Combinatorial structures and generating functions of Fishburn numbers, parking functions, and Tesler matrices	2012	Paul Levande
+ PDF Chat	Heronian Friezes	2020	Sergey Fomin Linus Setiabrata
+ PDF Chat	Perfect matching problems in cluster algebras and number theory	2024	Ralf Schiffler
+	Mini-Workshop: Friezes	2016	Thorsten Holm Peter Jørgensen Sophie Morier-Genoud
+	Frieze matrices and infinite frieze patterns with coefficients	2022	Juan Pablo Maldonado

Works That Cite This (93)

Action	Title	Year	Authors
+ PDF Chat	Mutation invariants of cluster algebras of rank 2	2024	Zhichao Chen Zixu Li
+ PDF Chat	On a rank-unimodality conjecture of Morier-Genoud and Ovsienko	2021	Thomas McConville Bruce E. Sagan Clifford Smyth
+	Mutation of type D friezes	2020	Ana García Elsener Khrystyna Serhiyenko
+ PDF Chat	Cluster expansion formulas and perfect matchings	2009	Gregg Musiker Ralf Schiffler
+ PDF Chat	Linear difference equations, frieze patterns, and the combinatorial Gale transform	2014	Sophie Morier-Genoud Valentin Ovsienko Richard Evan Schwartz Serge Tabachnikov
+	Arithmetic infinite friezes from punctured discs	2015	Manuela Tschabold
+	On a rank-unimodality conjecture of Morier-Genoud and Ovsienko	2020	Thomas McConville Bruce E. Sagan Clifford Smyth
+	$SL_2(\mathbb{Z})$-tilings of the torus, Coxeter-Conway friezes and Farey triangulations	2014	Sophie Morier-Genoud Valentin Ovsienko Serge Tabachnikov
+ PDF Chat	On Cluster Algebras Arising from Unpunctured Surfaces	2009	Ralf Schiffler Hugh Thomas
+	Extensions in Jacobian Algebras and Cluster Categories of Marked Surfaces	2014	̛İlke Çanakçı Sibylle Schroll

Works Cited by This (17)

Action	Title	Year	Authors
+	The Sensual (Quadratic) Form	2009	John H. Conway Francis Y. C. Fung
+ PDF Chat	Triangulated polygons and frieze patterns	1973	John H. Conway H. S. M. Coxeter
+	A combinatorial approach to matrix algebra	1985	Doron Zeilberger
+ PDF Chat	Billiards on rational-angled triangles	2000	Richard Kenyon John Smillie
+	The geometry of frieze patterns	1974	Duane M Broline Donald W. Crowe I. M. Isaacs
+	Binomial determinants, paths, and hook length formulae	1985	Ira M. Gessel Gérard Viennot
+	Theory of Resonance Topology of Fully Aromatic Hydrocarbons. I	1952	Mark S. Gordon W. H. T. Davison
+	Pythagorean primes and palindromic continued fractions.	2005	Arthur T. Benjamin Doron Zeilberger
+ PDF Chat	Counting on Continued Fractions	2000	Arthur T. Benjamin Francis Edward Su Jennifer J. Quinn
+ PDF Chat	Cluster algebras as Hall algebras of quiver representations	2006	Philippe Caldero Frédéric Chapoton