Completely symmetric configurations for σ-games on grid graphs

Mathieu Florence; Frédéric Meunier

doi:10.1007/s10801-009-0199-7

Completely symmetric configurations for σ-games on grid graphs

Mathieu Florence
, Frédéric Meunier

Research output: Contribution to journal › Article › peer-review

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 ≥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.

Original language	English
Pages (from-to)	533-545
Number of pages	13
Journal	Journal of Algebraic Combinatorics
Volume	31
Issue number	4
DOIs	https://doi.org/10.1007/s10801-009-0199-7
Publication status	Published - 1 Jun 2010
Externally published	Yes

Keywords

Chebychev polynomials
Commutative algebra
Sigma-games

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10.1007/s10801-009-0199-7

Cite this

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AB - 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.

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KW - Sigma-games

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Completely symmetric configurations for σ-games on grid graphs

Abstract

Keywords

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