Title: Impartial Avoidance and Achievement Games For Generating Finite Groups
Speaker: Nandor Sieben, DIMACS and Northern Arizona University
Date: Tuesday, November 4, 2014 12:00 - 1:00pm
Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ
Seminar hosted by James Abello, DIMACS
Abstract:
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