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Note on the Lamp Lighting Problem

✍ Scribed by Henrik Eriksson; Kimmo Eriksson; Jonas Sjöstrand

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 143 KB
Volume: 27
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.2001.0739

No coin nor oath required. For personal study only.

✦ Synopsis

We answer some questions concerning the so-called σ-game of Sutner [Linear cellular automata and the Garden of Eden, Math. Intelligencer 11 (1989), 49-53]. It is played on a graph where each vertex has a lamp, the light of which is toggled by pressing any vertex with an edge directed to the lamp. For example, we show that every configuration of lamps can be lit if and only if the number of complete matchings in the graph is odd. In the special case of an orthogonal grid one gets a criterion for whether the number of monomer-dimer tilings of an m × n grid is odd or even.

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