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PIVOTAL INVERSIONS OF A FINITE POINT-SET
http://hdl.handle.net/10131/5784
http://hdl.handle.net/10131/5784475e1ef0-75e5-4d60-9652-10a3e928b43f
名前 / ファイル | ライセンス | アクション |
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YMJ_53_N2_2007_119-126.pdf (700.6 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 | PIVOTAL INVERSIONS OF A FINITE POINT-SET | |||||
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 |
Maehara, Hiroshi
× Maehara, Hiroshi× Ueda, Sumie |
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著者所属 | ||||||
College of Education, Ryukyu University, Nishihara, Okinawa, Japan | ||||||
著者所属 | ||||||
The Institute of Statistical Mathematics, Minami-Azabu, Tokyo, Japan, | ||||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | For two distinct points $P,$ $Q$ in the plane, let $Q^{P}$ denote the point on the ray $¥overline{PQ}$ such that $PQ¥cdot PQ^{P}=1$ , and let $P^{P}=P$. For a point-set $¥tau$ in the plane and $ P¥in¥tau$ , define $¥tau^{P}=¥{Q^{P}|Q¥in¥tau¥}$ . The transformation $¥tau¥rightarrow¥tau^{P}$ is called the pivotal inversion at $ P¥in¥tau$ . We show that if $n¥geq 4$ then starting from any n-point-set, it is possible, by applying a sequence of pivotal inversions, to produce an n-point-set whose diameter exceeds any prescribed value, but it is impossible to produce more than $n+1$ mutually non-similar $n-point-sets$ . The latter part is proved by showing a group induced by pivotal inversions of ordered $n-point$-sets is isomorphic to the symmetric group of degree $n+1$ . | |||||
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. 119-126, 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 |