M. Kazarian, S. Lando
Published 2015-12-22Version 1
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.
Comments: 32 pages
Journal: Russian version: Uspekhi Mat. Nauk 70 (2015), no. 3(423), 77-106. English translation: 2015 Russ. Math. Surv. 70 453-482
Generalized Higher Specht Polynomials and Homogeneous Representations of Symmetric Groups
Extremes of generalized inversions on symmetric groups
Walks on the slit plane: other approaches
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