关键词: 群作用于集合, 容斥原理, Burnside-Polya计数法, 映射, 等价类, 组合恒等式

Abstract:

By using Burnside-Polya enumerating method, principle of inclusion-exclusion and other combinatorial analysis, a class of combinatorial identities for equivalent classes with action of group on set are studied. Some combinatorial identities for enumerations of equivalent classes of a class of mapping under identical transformation group and cycle group and dihedral group actions are obtained. These results generalize some known results.

Key words: action of group on set, principle of inclusion-exclusion, Burnside-Polya enumerating method, mapping, equivalent class, combinatorial identities