Note on the lamp lighting problem

Details Note on the lamp lighting problem Note on the lamp lighting problem

2004-11-09

arxiv.org/abs/math/0411201v1

Advances of Applied Mathematics 27, 2001, pages 357-366

Mathematics

Combinatorics

10 pages

Scientific paper

We answer some questions concerning the so called sigma-game 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 monomer-dimer tilings of an m times n grid is odd or even.

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