Regular Article
Note on the Lamp Lighting Problem

https://doi.org/10.1006/aama.2001.0739Get rights and content
Under an Elsevier user license
open archive

Abstract

We answer some questions concerning the so-called σ-game of Sutner [Linear cellular automata and the Garden of Eden, Math. Intelligencer11 (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.

Cited by (0)