P. E. Naryshkin, “A remark on the isomorphism between the Bernoulli scheme and the Plancherel measure”, Zap. Nauchn. Sem. POMI, 2018, Volume 468,Pages <nobr>98

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A remark on the isomorphism between the Bernoulli scheme and the Plancherel measure

P. E. Naryshkin

St. Petersburg State University, St. Petersburg, Russia

Abstract: 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.

Key words and phrases: Young tableau, Robinson–Schensted–Knuth algorithm, Plancherel measure, measurable partitions, Knuth equivalence.

UDC: 519.1

Received: 22.09.2018