Coxeter's frieze patterns at the crossroads of algebra, geometry and combinatorics

Abstract

Frieze patterns of numbers, introduced in the early 70's by Coxeter, are currently attracting much interest due to connections with the recent theory of cluster algebras. The present paper aims to review the original work of Coxeter and the new developments around the notion of frieze, focusing on the representation theoretic, geometric and combinatorial approaches.

References in corpus (8)

• Cluster algebras II: Finite type classification
• Functional Relations in Solvable Lattice Models I: Functional Relations and Representation Theory
• Graded quiver varieties, quantum cluster algebras and dual canonical basis
• Cyclic Sieving of Increasing Tableaux and small Schröder Paths
• SL_2-tilings and triangulations of the strip
• Categorification of a frieze pattern determinant
• Generalized frieze pattern determinants and higher angulations of polygons
• T-systems and the pentagram map

Cited by in corpus (10)

• Rotundus: triangulations, Chebyshev polynomials, and Pfaffians
• Frieze patterns with coefficients
• Friezes satisfying higher SL${}_k$-determinants
• Frieze patterns and Farey complexes
• Cluster algebras and binary subwords
• From frieze patterns to cluster categories
• Linear relations for Laurent polynomials and lattice equations
• A note on friezes of type ${\Lambda }_p$
• When frieze patterns meet Y-systems: Y-frieze patterns
• Classifying SL${}_2$-tilings