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ID 115957
著者
Koyama, Yuya Tokushima University
資料タイプ
紀要論文
抄録
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.
掲載誌名
Journal of Mathematics
ISSN
13467387
cat書誌ID
AA11595324
出版者
TOKUSHIMA UNIVERSITY
54
開始ページ
93
終了ページ
104
並び順
93
発行日
2020
EDB ID
フルテキストファイル
言語
eng
著者版フラグ
出版社版
部局
理工学系