Abstract

WEISS, Christian. Deducing Three Gap Theorem from Rauzy-Veech induction. Rev.colomb.mat. [online]. 2020, vol.54, n.1, pp.31-37. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v54n1.89777.

The Three Gap Theorem states that there are at most three distinct lengths of gaps if one places n points on a circle, at angles of z, 2z, … nz from the starting point. The theorem was first proven in 1958 by Sós and many proofs have been found since then. In this note we show how the Three Gap Theorem can easily be deduced by using Rauzy-Veech induction.

Keywords : Three Gap Theorem; Rauzy-Veech induction; Kronecker sequence; interval exchange transformation; uniform distribution.

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