Geodesic
Combinatorial solutions to integrable hierarchies
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 3, pp. 453-482
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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. Bibliography: 34 titles.
Keywords: integrable systems, Kadomtsev–Petviashvili hierarchy, Toda lattice hierarchy, Hurwitz numbers.
Mots-clés : boson-fermion correspondence 
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M. È. Kazarian; S. K. Lando. Combinatorial solutions to integrable hierarchies. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 3, pp. 453-482. http://geodesic.mathdoc.fr/item/RM_2015_70_3_a1/

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