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We show that every transformation is disjoint from almost every intervalexchange transformation (IET), answering a question of Bufetov. In particular,we prove that almost every pair of IETs is disjoint. It follows that theproduct of almost every pair is uniquely ergodic. A key step in the proof isshowing that any sequence of density 1 contains a rigidity sequence for almostevery IET, strengthening a result of Veech.

Every transformation is disjoint from almost every IET