Geodesic
A remark on the isomorphism between the Bernoulli scheme and the Plancherel measure
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 98-104

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We formulate a theorem of Romik and Śniady which establishes an isomorphism between the Bernoulli scheme and the Plancherel measure. Then we derive from it several combinatorial results. 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. M. Vershik. 
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     author = {P. E. Naryshkin},
     title = {A remark on the isomorphism between the {Bernoulli} scheme and the {Plancherel} measure},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {98--104},
     publisher = {mathdoc},
     volume = {468},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a8/}
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P. E. Naryshkin. A remark on the isomorphism between the Bernoulli scheme and the Plancherel measure. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 98-104. http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a8/