Completely symmetric configurations for sigma-games on grid graphs
Combinatorics
2009-03-03 v2 Rings and Algebras
Abstract
The paper deals with sigma-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 greater than or equal to 3, the answer is complete for the sigma^+ -game, and for the sigma^- -game if at least one of the sizes is even. The case sigma^-, dimension greater than or equal to 3 and all sizes odd remains open.
Keywords
Cite
@article{arxiv.0903.0339,
title = {Completely symmetric configurations for sigma-games on grid graphs},
author = {Mathieu Florence and Frédéric Meunier},
journal= {arXiv preprint arXiv:0903.0339},
year = {2009}
}
Comments
The bibliography has been corrected