This article is cited in 3 papers

Set partitions and integrable hierarchies

V. E. Adler

Landau Institute for Theoretical Physics of RAS, Chernogolovka, Moscow Oblast, Russia

Abstract: We demonstrate that statistics for several types of set partitions are described by generating functions arising in the theory of integrable equations.

Keywords: set partition, $B$-type partition, nonoverlapping partition, atomic partition, Bell polynomial, Dowling number, Bessel number, generating function, integrable hierarchy.

Received: 05.10.2015

DOI: 10.4213/tmf9051

 English version: Theoretical and Mathematical Physics, 2016, 187:3, 842–870

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