Interdisciplinary Series, Tuesday, November 4, 2014 12:00 – 1:00pm
Location: CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ
Title: Impartial Avoidance and Achievement Games For Generating Finite Groups
Speaker: Nandor Sieben, DIMACS and Northern Arizona University
We study two impartial games introduced by Anderson and Harary and further developed by Barnes. Both games are played by two players who alternately select previously unselected elements of a finite group. The first player who builds a generating set from the jointly selected elements wins the first game. The first player who cannot select an element without building a generating set loses the second game. We determine the nim-numbers of these games for abelian and dihedral groups. The main computational and theoretical tool is the structure diagram of a game, which is a type of identification digraph of the game digraph that is compatible with the nim-numbers of the positions. Structure diagrams also provide simple visualizations of these games that capture the complexity of the positions.
This is join work with Dana Ernst