Combinatorial solutions to integrable hierarchies
M. Kazarian, S. Lando
TL;DR
This paper reviews modern combinatorial methods for constructing formal solutions to integrable hierarchies, highlighting their connections to symmetric group combinatorics and applications in quantum field theory computations.
Contribution
It provides a comprehensive overview of combinatorial approaches to integrable hierarchies and their applications in mathematical physics.
Findings
Connections between integrable hierarchies and symmetric group combinatorics
Methods for constructing formal solutions to integrable hierarchies
Applications to quantum field theory computations
Abstract
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and combinatorics of symmetric groups and their representations is explained. Applications of the results to constructing efficient computations in problems related to models of quantum field theories are given.
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