On the combinatorics of several integrable hierarchies
V.E. Adler

TL;DR
This paper reveals that the combinatorial properties of specific set partitions are governed by generating functions connected to well-known integrable hierarchies like Burgers, Ibragimov--Shabat, and Korteweg--de Vries.
Contribution
It establishes a novel link between combinatorics of set partitions and integrable hierarchies through generating functions.
Findings
Set partition statistics are described by integrable hierarchy-related generating functions.
Connections between combinatorics and integrable systems are demonstrated.
Provides a new perspective on the structure of set partitions.
Abstract
We demonstrate that statistics of certain classes of set partitions is described by generating functions related to the Burgers, Ibragimov--Shabat and Korteweg--de Vries integrable hierarchies.
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