Matrices Associated to 3-Interval Exchange Transformation and their Spectra

摘要

A three by three integer matrix M is said to have the MEME Property if MEM~T = ±E, where E =(-101_(-1 -10)~(011)).We characterize such matrices in terms of their spectra. In [1], the authors study matrices of morphisms preserving the family of words coding 3-interval exchange transformations. It is well known [2-4] that matrices of morphisms preserving sturmian words (i.e. words coding 2-interval exchange transformations with the maximal possible subword complexity) form the monoid.