On the combinatorics of several integrable hierarchies

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.

arXiv comment16 pages

References in corpus (2)

• Integrability of Hurwitz Partition Functions. I. Summary
• Bernoulli numbers and solitons

Cited by in corpus (3)

• Integrable hierarchies, Hurwitz numbers and a branch point field in critical topologically massive gravity
• Green's functions and the Cauchy problem of the Burgers hierarchy and forced Burgers equation
• From Hurwitz numbers to Feynman diagrams: counting rooted trees in log gravity