2014/06/16 by Dolce, Francesco
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.1406.4075
We describe a generalization of a result of Boshernitzan and Carroll: an extension of Lagrange's Theorem on continued fraction expansion of quadratic irrationals to interval exchange transformations. In order to do this, we use a two-sided version of the Rauzy induction. In particular, we show that starting from an interval exchange transforma- tion whose lengths are defined over a quadratic field and applying the two-sided Rauzy induction, one can obtain only a finite number of new transformations up to homothety.