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A typical interval exchange transformation has an infinite sequence ofmatrices associated to it by successive iterations of Rauzy induction. In 2010,W. A. Veech answered a question of A. Bufetov by showing that the intervalexchange itself may be recovered from these matrices and must be unique up totopological conjugation. In this work, we will improve upon these results byproviding an algorithm to determine the initial transformation from asufficiently long finite subsequence of these matrices. We also show thedefined length to be necessary by constructing finite sequences of Rauzyinduction with multiple distinct (even up to conjugacy) initialtransformations.

Decoding Rauzy Induction: An Effective Answer to Bufetov's Question