期刊名称:International Journal of Mathematics and Mathematical Sciences
印刷版ISSN:0161-1712
电子版ISSN:1687-0425
出版年度:1982
卷号:5
DOI:10.1155/S0161171282000696
出版社:Hindawi Publishing Corporation
摘要:By using Pólya's theorem of enumeration and de Bruijn's generalization of Pólya's theorem, we obtain the numbers of various weak equivalence classes of functions in RD relative to permutation groups G and H where RD is the set of all functions from a finite set D to a finite set R, G acts on D and H acts on R. We present an algorithm for obtaining the equivalence classes of functions counted in de Bruijn's theorem, i.e., to determine which functions belong to the same equivalence class. We also use our algorithm to construct the family of non-isomorphic fm-graphs relative to a given group.