JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (8): 67-75.doi: 10.6040/j.issn.1671-9352.0.2020.153

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Enumerations of equivalent classes with actions of permutation group on a class of mapping set

TANG Shan-gang   

  1. School of Mathematics and Information, China West Normal University, Nanchong 637009, Sichuan, China
  • Published:2021-08-09

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Abstract: Enumerations of equivalent classes with action of permutation group on a class of mapping set are studied by using Burnside-Polya enumerating theorem, principle of inclusion-exclusion and other combinatorial analysis. Enumerations of equivalent classes and its plane circular alternating permutation enumerations, space circular alternating permutation enumerations and combinatorial identities with actions of cycle group and dihedral group on a class of mapping set are obtained. These results generalize some known results.

Key words: permutation group, principle of inclusion-exclusion, Burnside-Polya enumerating theorem, mapping, equivalent class, combinatorial identities

CLC Number: 

  • O157.1
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