Abelian property of the chip-firing game

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Theorem [1]. From a given initial chip-distribution, either every legal game can be continued indefinitely, or every legal game terminates after finitely many steps. The firing vector of every maximal legal game is the same.


  1. A. Björner, L. Lovász, P. Shor, Chip-firing games on graphs, (1991), DOI link, Author link