Variant of Wythoff's Game-Corner Two Rooks

• Item type: Journal(1)
• 公開日: 2020-12-15
• タイトル: Variant of Wythoff's Game-Corner Two Rooks
• タイトル / 言語: en
• タイトル: Variant of Wythoff's Game-Corner Two Rooks
• 言語: eng
• キーワード / 主題Scheme: Other
• キーワード / 主題: [特集：離散と計算の幾何・グラフ・ゲーム] Combinatorial game theory, Nim, Impartial games, Misère games
• 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: journal article
• 著者所属: Kwansei Gakuin
• 著者所属: Kwansei Gakuin
• 著者所属: Kwansei Gakuin
• 著者所属: National Institute of Informatics
• 著者所属(英): en
• 著者所属(英): Kwansei Gakuin
• 著者所属(英): en
• 著者所属(英): Kwansei Gakuin
• 著者所属(英): en
• 著者所属(英): Kwansei Gakuin
• 著者所属(英): en
• 著者所属(英): National Institute of Informatics
• 著者名: Kai, Hirokawa; Ryohei, Miyadera; Yusuke, Sakamoto; Koki, Suetsugu
• 著者名(英): Kai, Hirokawa; Ryohei, Miyadera; Yusuke, Sakamoto; Koki, Suetsugu
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: This article presents an impartial game, “Corner Two Rooks.” This game is a variant of “Corner the Queen” that is mathematically equivalent to Wythoff's game. In “Corner the Queen, ” a single chess queen is placed on a large grid of squares. Each player can move the queen any number of steps toward the upper-left corner of the grid, vertically, horizontally, or diagonally. The player who moves the queen into the upper-left corner is the winner. In this work, the authors use two rooks of chess instead of the queen, and a rook can jump over another rook but not onto another. There is a restriction on the distance that a rook can travel in each turn. This game can be considered as a misère game of the traditional Nim game with four piles and a restriction of the number of stones to be removed in each turn. The authors present the set of P-positions of the game using a theorem for misère games. When there is no restriction on the distance that a rook can travel in each turn, we obtain a similar result in which the set of P-positions is simpler.; ------------------------------; This is a preprint of an article intended for publication Journal of; Information Processing(JIP). This preprint should not be cited. This; article should be cited as: Journal of Information Processing Vol.28(2020) (online); DOI http://dx.doi.org/10.2197/ipsjjip.28.970; ------------------------------
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: This article presents an impartial game, “Corner Two Rooks.” This game is a variant of “Corner the Queen” that is mathematically equivalent to Wythoff's game. In “Corner the Queen, ” a single chess queen is placed on a large grid of squares. Each player can move the queen any number of steps toward the upper-left corner of the grid, vertically, horizontally, or diagonally. The player who moves the queen into the upper-left corner is the winner. In this work, the authors use two rooks of chess instead of the queen, and a rook can jump over another rook but not onto another. There is a restriction on the distance that a rook can travel in each turn. This game can be considered as a misère game of the traditional Nim game with four piles and a restriction of the number of stones to be removed in each turn. The authors present the set of P-positions of the game using a theorem for misère games. When there is no restriction on the distance that a rook can travel in each turn, we obtain a similar result in which the set of P-positions is simpler.; ------------------------------; This is a preprint of an article intended for publication Journal of; Information Processing(JIP). This preprint should not be cited. This; article should be cited as: Journal of Information Processing Vol.28(2020) (online); DOI http://dx.doi.org/10.2197/ipsjjip.28.970; ------------------------------
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AN00116647
• 書誌情報: 情報処理学会論文誌; 巻 61, 号 12, 発行日 2020-12-15
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 1882-7764