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

Author:

MORIER-GENOUD SOPHIE,OVSIENKO VALENTIN,EVAN SCHWARTZ RICHARD,TABACHNIKOV SERGE

Abstract

AbstractWe 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.

Publisher

Cambridge University Press (CUP)

Subject

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

Reference46 articles.

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