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

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

doi:10.1017/fms.2014.20

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

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

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22 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 language	English (US)
Article number	e22
Journal	Forum of Mathematics, Sigma
Volume	2
DOIs	https://doi.org/10.1017/fms.2014.20
State	Published - 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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10.1017/fms.2014.20

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AB - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

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