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Uspekhi Mat. Nauk, 2015, Volume 70, Issue 3(423), Pages 77–106 (Mi umn9661)  

This article is cited in 4 scientific papers (total in 4 papers)

Combinatorial solutions to integrable hierarchies

M. È. Kazarianab, S. K. Landob

a Steklov Mathematical Institute of Russian Academy of Sciences
b National Research University Higher School of Economics

Abstract: 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.
Bibliography: 34 titles.

Keywords: integrable systems, Kadomtsev–Petviashvili hierarchy, Toda lattice hierarchy, boson-fermion correspondence, Hurwitz numbers.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00383-а


DOI: https://doi.org/10.4213/rm9661

Full text: PDF file (667 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2015, 70:3, 453–482

Bibliographic databases:

Document Type: Article
UDC: 512.542.74+515.162.2+517.958:530.145
MSC: Primary 14H70, 37K20, 81R12; Secondary 57R56
Received: 25.12.2014

Citation: M. È. Kazarian, S. K. Lando, “Combinatorial solutions to integrable hierarchies”, Uspekhi Mat. Nauk, 70:3(423) (2015), 77–106; Russian Math. Surveys, 70:3 (2015), 453–482

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Alexandrov, D. Lewanski, S. Shadrin, “Ramifications of Hurwitz theory, KP integrability and quantum curves”, J. High Energy Phys., 2016, no. 5, 124, 30 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    2. P. Zograf, M. Kazarian, “Rationality in map and hypermap enumeration by genus”, St. Petersburg Math. J., 29:3 (2018), 439–445  mathnet  crossref  isi  elib
    3. S. M. Natanzon, A. Yu. Orlov, “BKP and projective Hurwitz numbers”, Lett. Math. Phys., 107:6 (2017), 1065–1109  crossref  mathscinet  zmath  isi  scopus
    4. Viet Anh Nguyen, “Explicit Formulae For One-Part Double Hurwitz Numbers With Completed 3-Cycles”, J. Algebr. Comb., 48:2 (2018), 307–323  crossref  mathscinet  isi  scopus
  • Успехи математических наук Russian Mathematical Surveys
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