Formal Definition
Let and let be a permutation on . Consider a vector
of positive real numbers (the widths of the subintervals), satisfying
Define a map
called the interval exchange transformation associated to the pair as follows. For
let
- and let
Then for, define
if lies in the subinterval . Thus acts on each subinterval of the form by an orientation-preserving isometry, and it rearranges these subintervals so that the subinterval at position is moved to position .
Read more about this topic: Interval Exchange Transformation
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