经典统计力学中幂级数系数表示的复杂性。它们的分类和复杂性标准
Complexity of representations of coefficients of power series in classical statistical mechanics. Their classification and complexity criteria
摘要：
指出经典统计力学幂级数系数简化表示的目的是简化利用其简化表示求系数估计的过程。文章的目的是：制定标准的复杂性（从上述角度来看），这些表示，并证明其应用的例子比较Ree-Hoover表示的维里系数和幂级数系数的这种表示的基础上的概念的框架分类的标记图。为了解决这些问题，引入了数学概念（如基积、基积分、积分的基线性组合、复杂系数可忽略的积分的基线性组合、复杂系数可忽略的积分的基线性组合的基集），并提出了经典统计力学幂级数系数表示的分类。在这一分类中，复杂性系数可忽略的积分的基线性组合类是最重要的一类。它包括经典统计力学的幂级数系数的最著名的表示。给出了可忽略系数积分基线性组合的相对复杂性的三个估计准则，并将其推广到可忽略系数积分基线性组合的基集的总体上.通过比较上述幂级数系数表示的例子，说明了所有构造的准则的应用。所获得的结果列于表中并进行了评论。
英文摘要：
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 these representations and to demonstrate their application by examples of comparing Ree-Hoover representations of virial coefficients and such representations of power series coefficients that are based on the conception of the frame classification of labeled graphs. To solve these problems, mathematical notions were introduced (such as a base product, a base integral, a base linear combination of integrals, a base linear combination of integrals with coefficients of negligible complexity, a base set of base linear combinations of integrals with coefficients of negligible complexity); and a classification of representations of coefficients of power series of classical statistical mechanics is proposed. In this classification the class of base linear combinations of integrals with coefficients of negligible complexity is the most important class. It includes the most well-known representations of the coefficients of power series of classical statistical mechanics. Three criteria are formulated to estimate the comparative complexity of base linear combinations of integrals with coefficients of negligible complexity and their extensions to the totality of base sets of base linear combinations of integrals with coefficients of negligible complexity are constructed. The application of all the constructed criteria is demonstrated by examples of comparing with each other of the above power series coefficients representations. The obtained results are presented in the tables and commented.
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