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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Hindawi Limited
2021
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oai:doaj.org-article:d4ba643404bc434583368b34cd2238972021-11-08T02:35:31ZOn the Number of Conjugate Classes of Derangements2314-478510.1155/2021/6023081https://doaj.org/article/d4ba643404bc434583368b34cd2238972021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/6023081https://doaj.org/toc/2314-4785The 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.Wen-Wei LiZhong-Lin ChengJia-Bao LiuHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021) |
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DOAJ |
| collection |
DOAJ |
| language |
EN |
| topic |
Mathematics QA1-939 |
| spellingShingle |
Mathematics QA1-939 Wen-Wei Li Zhong-Lin Cheng Jia-Bao Liu On the Number of Conjugate Classes of Derangements |
| 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 |
| 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 |
| title |
On the Number of Conjugate Classes of Derangements |
| title_short |
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_sort |
on the number of conjugate classes of derangements |
| publisher |
Hindawi Limited |
| publishDate |
2021 |
| url |
https://doaj.org/article/d4ba643404bc434583368b34cd223897 |
| work_keys_str_mv |
AT wenweili onthenumberofconjugateclassesofderangements AT zhonglincheng onthenumberofconjugateclassesofderangements AT jiabaoliu onthenumberofconjugateclassesofderangements |
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