Completely symmetric configurations for σ -games on grid graphs
Mathieu Florence
and Frédéric Meunier
DOI: 10.1007/s10801-009-0199-7
Abstract
The paper deals with σ -games on grid graphs (in dimension 2 and more) and conditions under which any completely symmetric configuration of lit vertices can be reached - in particular the completely lit configuration - when starting with the all-unlit configuration. The answer is complete in dimension 2. In dimension \geq 3, the answer is complete for the σ +-game, and for the σ - -game if at least one of the sizes is even. The case σ - , dimension \geq 3 and all sizes odd remains open.
Pages: 533–545
Keywords: keywords sigma-games; chebychev polynomials; commutative algebra
Full Text: PDF
References
1. Barua, R., Ramakrishnan, S.: σ- -game, σ+-game and two-dimensional additive cellular automata.
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