Set partitions and integrable hierarchies

V. E. Adler

doi:10.1134/S0040577916060052

Set partitions and integrable hierarchies

Authors: Adler V.E.¹
Affiliations:
1. Landau Institute for Theoretical Physics
Issue: Vol 187, No 3 (2016)
Pages: 842-870
Section: Article
URL: https://journals.rcsi.science/0040-5779/article/view/170641
DOI: https://doi.org/10.1134/S0040577916060052
ID: 170641

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Abstract
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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

About the authors

V. E. Adler

Landau Institute for Theoretical Physics

Author for correspondence.
Email: adler@itp.ac.ru
Russian Federation, Chernogolovka, Moscow Oblast

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