Note on the lamp lighting problem

• We answer some questions concerning the so-called sigma -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 x n grid is odd or even.

Ämnesord

NATURVETENSKAP  -- Matematik -- Diskret matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Discrete Mathematics (hsv//eng)

Nyckelord

cellular-automata

game

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