Combinatorial solutions to integrable hierarchies

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This paper reviews modern approaches to the construction of formal solutions to integrable hierarchies of mathematical physics whose coefficients are answers to various enumerative problems. The relationship between these approaches and the combinatorics of symmetric groups and their representations is explained. Applications of the results to the construction of efficient computations in problems related to models of quantum field theories are described.

Original languageEnglish
Pages (from-to)453-482
Number of pages30
JournalRussian Mathematical Surveys
Issue number3
Publication statusPublished - 2015
Externally publishedYes


  • Boson-Fermion correspondence
  • Hurwitz numbers
  • Integrable systems
  • Kadomtsev-Petviashvili hierarchy
  • Toda lattice hierarchy


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