Minimal Recurrent Configurations of Chip Firing Games and Directed Acyclic Graphs

Abstract : We discuss a very close relation between minimal recurrent configurations of Chip Firing Games and Directed Acyclic Graphs and demonstrate the usefulness of this relation by giving a lower bound for the number of minimal recurrent configurations of the Abelian Sandpile Model as well as a lower bound for the number of firings which are caused by the addition of two recurrent configurations on particular graphs.
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Fatès, Nazim and Kari, Jarkko and Worsch, Thomas. Automata 2010 - 16th Intl. Workshop on CA and DCS, 2010, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AL, Automata 2010 - 16th Intl. Workshop on CA and DCS, pp.111-124, 2010, DMTCS Proceedings
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Matthias Schulz. Minimal Recurrent Configurations of Chip Firing Games and Directed Acyclic Graphs. Fatès, Nazim and Kari, Jarkko and Worsch, Thomas. Automata 2010 - 16th Intl. Workshop on CA and DCS, 2010, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AL, Automata 2010 - 16th Intl. Workshop on CA and DCS, pp.111-124, 2010, DMTCS Proceedings. 〈hal-01185492〉

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