Journal of Algebraic Combinatorics

, Volume 31, Issue 4, pp 533–545 | Cite as

Completely symmetric configurations for σ-games on grid graphs

  • Mathieu Florence
  • Frédéric Meunier


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 ≥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 ≥3 and all sizes odd remains open.


Sigma-games Chebychev polynomials Commutative algebra 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Equipe de Topologie et Géométrie AlgébriquesUniversité Paris 6ParisFrance
  2. 2.LVMT, ENPCUniversité Paris EstMarne-la-Vallée cedex 2France

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