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Theoretical and Mathematical Physics

, Volume 187, Issue 3, pp 842–870 | Cite as

Set partitions and integrable hierarchies

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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 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsChernogolovka, Moscow OblastRussia

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