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ON THE SWITCHBACK VERTION OF JOSEPHUS PROBLEM
http://hdl.handle.net/10131/5785
http://hdl.handle.net/10131/5785ef13a837-4ca2-43d2-a85d-1a6156a4f9dd
名前 / ファイル | ライセンス | アクション |
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YMJ_53_N2_2007_083-088.pdf (444.7 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2009-12-15 | |||||
タイトル | ||||||
タイトル | ON THE SWITCHBACK VERTION OF JOSEPHUS PROBLEM | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
著者 |
Matsumoto, Keiichi
× Matsumoto, Keiichi× Nakamigawa, Tomoki× Watanabe, Mamoru |
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著者所属 | ||||||
Department of Computer Science and Mathematics, Kurashiki University of Science and the Arts, Japan | ||||||
著者所属 | ||||||
Department of Mathematics, Keio University, Japan | ||||||
著者所属 | ||||||
Department of Computer Science and Mathematics, Kurashiki University of Science and the Arts,Japan | ||||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | In this paper we will study an alternative row version of Josephus problem. Suppose that $n$numbers 1, 2, $¥cdot$ . . , $n$ are arranged in a line from left to right in this order. Starting with number 1, and counting each number from left to right, every second number is eliminated. Subsequently, starting with the right most number of the remains and counting each number in turn in the contrary direction, $i.e$ . from right to left, every second number is eliminated. Repeat such a process by alternate changing the order of cunting and eliminating until only one number is left. Denote by $f_{t}(n)$ the number of the $(n-t+1)$-th element which is removed by the process described above. If $n' s$ binary expansion is $¥sum_{k=0}^{¥infty}2^{k}n_{k}(n_{k}=1,0)$ , let us denote $f(n)=¥sum_{k=0}^{¥infty}2^{2k+1}n_{2k+1}$ . Let $g_{t}(n)$ be either $0$ for $t=1$ , or $(-2)^{r}¥{f(¥sigma^{r}(2n-1))+f(¥sigma^{r}(n-1))-2t+3¥}$ for $t¥geq 2$ , where $ r=¥lfloor¥log_{2}¥frac{n-1}{t-1}¥rfloor$ and $¥sigma(n)=L¥frac{n}{2}¥rfloor$ , i.e. $¥sigma(n)$ is one-bit shift right of $n' s$ binary expansion. In this paper we prove that $f_{t}(n)=f(n-1)+1+g_{t}(n)$ . | |||||
書誌情報 |
Yokohama Mathematical Journal = 横濱市立大學紀要. D部門, 数学 巻 53, 号 2, p. 83-88, 発行日 2007 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 00440523 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA0089285X | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
出版者 | ||||||
出版者 | Yokohama City University and Yokohama National University |