  It is declared that the aim of simplifying representations of coefficients of
power series of classical statistical mechanics is to simplify a process of
obtaining estimates of the coefficients using their simplified representations.
The aim of the article is: to formulate criteria for the complexity (from the
above point of view) of representations of coefficients of the power series of
classical statistical mechanics and to demonstrate their application by
examples of comparing the Ree-Hoover representations of virial coefficients
(briefly -- the RH representations) with such representations of power series
coefficients that are based on the conception of the frame classification of
labeled graphs (the abbreviation -- FC). To solve these problems, mathematical
notions were introduced (such as a basic product, a basic integral, a basic
linear combination, a basic linear combination with coefficients of
insignificant complexity(the abbreviation -- BLC with CIC) and the
classification of representations of the coefficients of power series of
classical statistical mechanics is proposed. In the classification, the class
of BLC's with CIC is the most important. It includes all the above
representations of the coefficients of power series of classical statistical
mechanics. Three criteria are formulated for estimate the comparative
complexity of BLC's with CIC. These criteria are ordered by their accuracy.
Based on each of these criteria, a criterion for the comparative complexity of
finite sets of BLC's with CIC is constructed. The constructed criteria are
ordered by their accuracy. The application of all the constructed criteria is
demonstrated by examples of comparing RH representations with the
representations of the power series coefficients based on the concept FC. The
obtained results are presented in the tables and commented.
