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TMF, 2016, Volume 187, Number 3, Pages 455–486 (Mi tmf9051)  

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

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00289_a
This research was supported by the Russian Foundation for Basic Research (Grant No. 16-01-00289_a).


DOI: https://doi.org/10.4213/tmf9051

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

Bibliographic databases:

Received: 05.10.2015

Citation: V. E. Adler, “Set partitions and integrable hierarchies”, TMF, 187:3 (2016), 455–486; Theoret. and Math. Phys., 187:3 (2016), 842–870

Citation in format AMSBIB
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