Seminar Series: Impartial Avoidance and Achievement Games For Generating Finite Groups, November 4, 2014

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

 

Abstract

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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

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