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Graphs and Algebras of Symmetric Functions

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Abstract

We describe an algebraic technique for operating with power series whose coefficients are represented by integrals of symmetric functions fn defined on the Cartesian powers Ωn of a set Ω with a measure μ. Moreover, each of the coefficient functions fn is obtained by means of a special mapping from graphs with n labeled vertices belonging to a fixed class. This technique has application to equilibrium statistical mechanics and to problems of enumeration of graphs.

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Authors and Affiliations

  1. Belgorod State University, Belgorod, Russia

    Yu. P. Virchenko & L. P. Danilova

Authors
  1. Yu. P. Virchenko
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  2. L. P. Danilova
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Correspondence to Yu. P. Virchenko.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 174, Geometry and Mechanics, 2020.

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Virchenko, Y.P., Danilova, L.P. Graphs and Algebras of Symmetric Functions. J Math Sci 272, 642–657 (2023). https://doi.org/10.1007/s10958-023-06461-7

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  • DOI: https://doi.org/10.1007/s10958-023-06461-7

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