Linear difference equations, frieze patterns, and the combinatorial Gale transform

Sophie Morier-Genoud, Valentin Ovsienko, Richard Evan Schwartz, Serge Tabachnikov

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We study the space of linear difference equations with periodic coefficients and (anti)periodic solutions. We show that this space is isomorphic to the space of tame frieze patterns and closely related to the moduli space of configurations of points in the projective space. We define the notion of a combinatorial Gale transform, which is a duality between periodic difference equations of different orders. We describe periodic rational maps generalizing the classical Gauss map.

Original languageEnglish (US)
Article numbere22
JournalForum of Mathematics, Sigma
Volume2
DOIs
StatePublished - Feb 1 2014

All Science Journal Classification (ASJC) codes

  • Analysis
  • Theoretical Computer Science
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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