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Square, Rectangular and Triangular Nim Games
https://tokushima-u.repo.nii.ac.jp/records/2008880
https://tokushima-u.repo.nii.ac.jp/records/20088804dbbbfce-4b57-41a2-9f9f-8ef58709068a
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jm_54_93.pdf (386 KB)
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| Item type | 文献 / Documents(1) | |||||||||||||||||
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| 公開日 | 2021-05-11 | |||||||||||||||||
| アクセス権 | ||||||||||||||||||
| アクセス権 | open access | |||||||||||||||||
| 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 | |||||||||||||||||
| 出版タイプ | ||||||||||||||||||
| 出版タイプ | VoR | |||||||||||||||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||||||||||||
| タイトル | ||||||||||||||||||
| タイトル | Square, Rectangular and Triangular Nim Games | |||||||||||||||||
| 著者 |
片山, 真一
× 片山, 真一
WEKO
1028
× コヤマ, ユウヤ
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| 抄録 | ||||||||||||||||||
| 内容記述 | Let p be an integer with p ≥ 2. We shall investigate the following two piles Nim games. Let S be the set of positive integers {1 ≤ i ≤ p − 1}. Each player can remove the number of tokens s1 ∈ {0} ∪ S from the first pile and s2 ∈ {0} ∪ S from the second pile with 0 < s1 + s2 at the same time. We shall identify (m, n) to a position of this Nim game, where m is the number of tokens in the first pile and n is the number of tokens in the second pile. We shall show the Sprague-Grundy sequence (or simply G-sequences) gs(m, n) satisfy the periodic relation gs(m+p, n+p) = gs(m, n) for any position (m, n). We will call this two piles Nim Square Nim. In case m and n are sufficiently large, we will show that G-sequences gs(m, n) are also periodic for each row and column with the same period p. Finally we shall introduce several related games, such as Rectangular Nim, Triangular Nim and Polytope Nim. | |||||||||||||||||
| 書誌情報 |
en : Journal of Mathematics 巻 54, p. 93-104, 発行日 2020 |
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| 収録物識別子タイプ | ISSN | |||||||||||||||||
| 収録物識別子 | 13467387 | |||||||||||||||||
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| 収録物識別子タイプ | NCID | |||||||||||||||||
| 収録物識別子 | AA11595324 | |||||||||||||||||
| 出版者 | ||||||||||||||||||
| 出版者 | TOKUSHIMA UNIVERSITY | |||||||||||||||||
| EID | ||||||||||||||||||
| 識別子 | 373578 | |||||||||||||||||
| 言語 | ||||||||||||||||||
| 言語 | eng | |||||||||||||||||
