Drawing Strategies for Generalized Tic-Tac-Toe (P, Q)
Proceedings of the International Conference on Progress in Applied Mathematics in Sciences and Engineering (PIAMSE2015),
AIP Conference Proceedings Vol.1705, 020021, pp.8 pages
(2015), [peer-reviewed]
Event Date:
September 28-October 1, 2015
Abstract / 概要
$GTTT(p, q)$ is an achievement game for polyominoes, which is an extension of Harary’s generalized tic-tac-toe. Two players alternately put $p$ stones over a board with the exception that the first player Black puts $q$ stones for the first move. The player who first achieves a given polyomino wins the game. Unlike the generalized tic-tac-toe, we define winner for polyomino that Black can achieve, loser that White can achieve, and draw that both players cannot achieve in each $GTTT(p, q)$. In this paper we define three classes of polyominoes for $GTTT(p, q)$ and show that any polyomino that satisfies some conditions for each classes is a draw.