
Mathematics 2004
Note on the lamp lighting problemAbstract: We answer some questions concerning the so called sigmagame of Sutner. 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 monomerdimer tilings of an m times n grid is odd or even.
