A Remark on the Isomorphism Between the Bernoulli Scheme and the Plancherel Measure

Аннотация

We formulate a theorem of Romik and Śniady that establishes an isomorphism between the Bernoulli scheme and the Plancherel measure. Then we derive several combinatorial results as corollaries. The first one is related to measurable partitions; the other two are related to the Knuth equivalence. We also give several examples and one conjecture belonging to A. Vershik.