Geodesic
Graphs and algebras of symmetric functions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 174 (2020), pp. 20-36

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We describe an algebraic technique for operating with power series whose coefficients are represented by integrals of symmetric functions $f_n$ defined on the Cartesian powers $\Omega^n$ of a set $\Omega$ with a measure $\mu$. Moreover, each of the coefficient functions $f_n$ 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.
Keywords: graph, commutative algebra, symmetric function, invariant measure, generating function, multiplicative functional. 
@article{INTO_2020_174_a2,
     author = {Yu. P. Virchenko and L. P. Danilova},
     title = {Graphs and algebras of symmetric functions},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {20--36},
     publisher = {mathdoc},
     volume = {174},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_174_a2/}
}
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Yu. P. Virchenko; L. P. Danilova. Graphs and algebras of symmetric functions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 174 (2020), pp. 20-36. http://geodesic.mathdoc.fr/item/INTO_2020_174_a2/