Variants of (s,t)-Wythoff’s game

• Published in: Discrete Applied Mathematics Vol. 227; pp. 1 - 12
• Main Authors: Li, Haiyan, Liu, Sanyang, Fraenkel, Aviezri S., Liu, Wen An
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 20.08.2017; Elsevier BV
• Subjects: [formula omitted]-position; [formula omitted]-Wythoff’s game; Applied mathematics; Combinatorics; Constrictions; Games; Normal play convention; Restriction; Restriction; Normal play convention; P-position; (s,t)-Wythoff’s game
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/j.dam.2017.04.020

In this paper, we study four games, they are all restrictions of (s,t)-Wythoff’s game which was introduced by A.S. Fraenkel. The first one is a modular type restriction of (s,t)-Wythoff’s game, where a player is restricted to remove a multiple of K tokens in each move (K is a fixed positive integer). The others we called rook type restrictions of (s,t)-Wythoff’s game, including Odd-Arbitrary-Nim (s,t)-Wythoff’s Game, Odd–Odd-Nim (s,t)-Wythoff’s Game and Odd–Even-Nim (s,t)-Wythoff’s Game. In these three games, the restrictions are only made on horizontal and vertical moves, but not on the extended diagonal moves. For any K,s,t≥1, the sets of P-positions of our games are given in both normal and misère play.