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It is declared that the aim of simplifying representations of coefficients ofpower series of classical statistical mechanics is to simplify a process ofobtaining estimates of the coefficients using their simplified representations.The aim of the article is: to formulate criteria for the complexity (from theabove point of view) of representations of coefficients of the power series ofclassical statistical mechanics and to demonstrate their application byexamples of comparing the Ree-Hoover representations of virial coefficients(briefly -- the RH representations) with such representations of power seriescoefficients that are based on the conception of the frame classification oflabeled graphs (the abbreviation -- FC). To solve these problems, mathematicalnotions were introduced (such as a basic product, a basic integral, a basiclinear combination, a basic linear combination with coefficients ofinsignificant complexity(the abbreviation -- BLC with CIC) and theclassification of representations of the coefficients of power series ofclassical statistical mechanics is proposed. In the classification, the classof BLC's with CIC is the most important. It includes all the aboverepresentations of the coefficients of power series of classical statisticalmechanics. Three criteria are formulated for estimate the comparativecomplexity of BLC's with CIC. These criteria are ordered by their accuracy.Based on each of these criteria, a criterion for the comparative complexity offinite sets of BLC's with CIC is constructed. The constructed criteria areordered by their accuracy. The application of all the constructed criteria isdemonstrated by examples of comparing RH representations with therepresentations of the power series coefficients based on the concept FC. Theobtained results are presented in the tables and commented.

Representations of coefficients of power series in classical statistical mechanics. Their classification and complexity criteria