Group Actions on Winning Games of Super Tic-Tac-Toe

2016/06/14 by Whitney George, George, Whitney, Janine E. Janoski +1 · 1 citation
Computer Science · Mathematics · #Artificial Intelligence in Games #Computability, Logic, AI Algorithms #Logic, programming, and type systems #math.CO

paper · pdf · doi:10.48550/arxiv.1606.04779

arxiv created 2016/06/14 · arxiv updated 2016/06/16

Abstract

Consider a n × n tic-tac-toe board. In each field of the board, draw a smaller n× n tic-tac-toe board. Now let super tic-tac-toe (STTT) be a game where each player's move dictates which field on the larger board a player must make their next move. We will play an impartial game of STTT where each player uses X. We define a set of actions on a game board which gives rise to a group-action on the game that creates equivalent games. We will discuss how the structure of this group-action forms a Dihedral group.

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