Two variants of Wythoff始s game preserving its -positions

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• 作者：Nhan Bao Ho ^{nbho@students.latrobe.edu.au honhanbao@yahoo.com}
• 关键词：Wythoff始s game ; P-positions ; Sprague&ndash ; Grundy function ; Combinatorial games
• 刊名：Journal of Combinatorial Theory ; Series A
• 出版年：2012
• 期刊代码：72_00973165
• 类别：mt
• 出版时间：August, 2012
• 卷：119
• 期：6
• 页码：1302-1314
• 文件大小：210 K

摘要

We present two variants of Wythoff始s game. The first game is a restriction of Wythoff始s game in which removing tokens from the smaller pile is not allowed if the two entries are not equal. The second game is an extension of Wythoff始s game obtained by adjoining a move allowing players to remove k tokens from the smaller pile and l tokens from the other pile provided . We show that both games preserve the -positions of Wythoff始s game. This resolves a question raised by Duch锚ne, Fraenkel, Nowakowski and Rigo. We give formulas for those positions which have Sprague-Grundy value 1. We also prove several results on the Sprague-Grundy functions.