On the Number of Conjugate Classes of Derangements
The number of conjugate classes of derangements of order n is the same as the number hn of the restricted partitions with every portion greater than 1. It is also equal to the number of isotopy classes of 2×n Latin rectangles. Sometimes the exact value is necessary, while sometimes we need the appro...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6023081 |
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| author | Wen-Wei Li Zhong-Lin Cheng Jia-Bao Liu |
| author_facet | Wen-Wei Li Zhong-Lin Cheng Jia-Bao Liu |
| author_sort | Wen-Wei Li |
| collection | DOAJ |
| description | The number of conjugate classes of derangements of order n is the same as the number hn of the restricted partitions with every portion greater than 1. It is also equal to the number of isotopy classes of 2×n Latin rectangles. Sometimes the exact value is necessary, while sometimes we need the approximation value. In this paper, a recursion formula of hn will be obtained and also will some elementary approximation formulae with high accuracy for hn be presented. Although we may obtain the value of hn in some computer algebra system, it is still meaningful to find an efficient way to calculate the approximate value, especially in engineering, since most people are familiar with neither programming nor CAS software. This paper is mainly for the readers who need a simple and practical formula to obtain the approximate value (without writing a program) with more accuracy, such as to compute the value in a pocket science calculator without programming function. Some methods used here can also be applied to find the fitting functions for some types of data obtained in experiments. |
| format | Article |
| id | doaj-art-d4ba643404bc434583368b34cd223897 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-d4ba643404bc434583368b34cd2238972025-02-03T00:58:55ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/6023081On the Number of Conjugate Classes of DerangementsWen-Wei Li0Zhong-Lin Cheng1Jia-Bao Liu2School of Information and MathematicsSchool of Information and MathematicsSchool of Mathematics and PhysicsThe number of conjugate classes of derangements of order n is the same as the number hn of the restricted partitions with every portion greater than 1. It is also equal to the number of isotopy classes of 2×n Latin rectangles. Sometimes the exact value is necessary, while sometimes we need the approximation value. In this paper, a recursion formula of hn will be obtained and also will some elementary approximation formulae with high accuracy for hn be presented. Although we may obtain the value of hn in some computer algebra system, it is still meaningful to find an efficient way to calculate the approximate value, especially in engineering, since most people are familiar with neither programming nor CAS software. This paper is mainly for the readers who need a simple and practical formula to obtain the approximate value (without writing a program) with more accuracy, such as to compute the value in a pocket science calculator without programming function. Some methods used here can also be applied to find the fitting functions for some types of data obtained in experiments.http://dx.doi.org/10.1155/2021/6023081 |
| spellingShingle | Wen-Wei Li Zhong-Lin Cheng Jia-Bao Liu On the Number of Conjugate Classes of Derangements Journal of Mathematics |
| title | On the Number of Conjugate Classes of Derangements |
| title_full | On the Number of Conjugate Classes of Derangements |
| title_fullStr | On the Number of Conjugate Classes of Derangements |
| title_full_unstemmed | On the Number of Conjugate Classes of Derangements |
| title_short | On the Number of Conjugate Classes of Derangements |
| title_sort | on the number of conjugate classes of derangements |
| url | http://dx.doi.org/10.1155/2021/6023081 |
| work_keys_str_mv | AT wenweili onthenumberofconjugateclassesofderangements AT zhonglincheng onthenumberofconjugateclassesofderangements AT jiabaoliu onthenumberofconjugateclassesofderangements |