Given a prescribed trajectory, is it possible to construct an interval exchange having this trajectory?
For example, given a 3-letter word (like aaabbbccabcaaa ), is it possible to construct a 3- interval exchange with a point having this word as the beginning of its trajectory?
what necessary conditions on a given word to be the trarjectory of a IET can be found?
For the relation between coding and interval exchange, see e.g. : http://combinat.sagemath.org/doc/reference/combinat/sage/combinat/iet/tutorial.html#orbit-and-symbolic-coding