Equivalence classes of functions on finite sets
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171282000696 |
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| _version_ | 1850225712683810816 |
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| author | Chong-Yun Chao Caroline I. Deisher |
| author_facet | Chong-Yun Chao Caroline I. Deisher |
| author_sort | Chong-Yun Chao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5ba908314ea34365ad468e253cd80dc7 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1982-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5ba908314ea34365ad468e253cd80dc72025-08-20T02:05:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251982-01-015474576210.1155/S0161171282000696Equivalence classes of functions on finite setsChong-Yun Chao0Caroline I. Deisher1Department of Mathematics, University of Pittsburgh, Pittsburgh 15260, PA, USADepartment of Mathematics, Indiana University of Pennsylvania, Indiana 15705, PA, USABy 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.http://dx.doi.org/10.1155/S0161171282000696enumerationsequivalence classes of functions on finite setsalgorithmfm-graphs. |
| spellingShingle | Chong-Yun Chao Caroline I. Deisher Equivalence classes of functions on finite sets International Journal of Mathematics and Mathematical Sciences enumerations equivalence classes of functions on finite sets algorithm fm-graphs. |
| title | Equivalence classes of functions on finite sets |
| title_full | Equivalence classes of functions on finite sets |
| title_fullStr | Equivalence classes of functions on finite sets |
| title_full_unstemmed | Equivalence classes of functions on finite sets |
| title_short | Equivalence classes of functions on finite sets |
| title_sort | equivalence classes of functions on finite sets |
| topic | enumerations equivalence classes of functions on finite sets algorithm fm-graphs. |
| url | http://dx.doi.org/10.1155/S0161171282000696 |
| work_keys_str_mv | AT chongyunchao equivalenceclassesoffunctionsonfinitesets AT carolineideisher equivalenceclassesoffunctionsonfinitesets |