Graphs and Algebras of Symmetric Functions

被引：0
|
作者：
Virchenko Y.P. [1 ]
Danilova L.P. [1 ]
机构：
[1] Belgorod State University, Belgorod
来源：
Journal of Mathematical Sciences | 2023年 / 272卷 / 5期
关键词：
05C30; 13A99; 82B05; commutative algebra; generating function; graph; invariant measure; multiplicative functional; symmetric function;
D O I：
10.1007/s10958-023-06461-7
中图分类号：
学科分类号：
摘要：
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. © 2023, Springer Nature Switzerland AG.
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页码：642 / 657
页数：15
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