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  1. Home > Articles & Issues >
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  3. Minimal Recurrent Co ...
Conference paper

Minimal Recurrent Configurations of Chip Firing Games and Directed Acyclic Graphs

Matthias Schulz (1) (2)
(1) Karlsruhe Institute of Technology
(2) Karlsruhe Institute of Technology = Karlsruher Institut für Technologie
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Imported on
January 31, 2017
Published on
December 31, 2009
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AL, Automata 2010 - 16th Intl. Workshop on CA and DCS
Proceedings
DOI
10.46298/dmtcs.2756
License
https://about.hal.science/hal-authorisation-v1
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Minimal Recurrent Configurations of Chip Firing Games and Directed Acyclic Graphs

Matthias Schulz (1) (2)
(1) Karlsruhe Institute of Technology
(2) Karlsruhe Institute of Technology = Karlsruher Institut für Technologie
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.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
  • [NLIN.NLIN-CG]Nonlinear Sciences [physics]/Cellular Automata and Lattice Gases [nlin.CG]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • Chip Firing Games
  • Sandpile Model
  • Minimal Recurrent Configurations
  • DAGs
  • Addition of Recurrent Configurations
Cited by

Source: OpenCitations

  • Feedback Arc Set Problem and NP-Hardness of Minimum Recurrent Configuration Problem of Chip-Firing Game on Directed Graphs

    arXiv (Cornell University)

    Authors : Kévin Perrot, Trung Van Pham ORCID

    Journal reference : Volume 19, 2015, pp. 373-396

    DOI : 10.1007/s00026-015-0266-9

  • EW-Tableaux, Le-Tableaux, Tree-Like Tableaux and the Abelian Sandpile Model

    The Electronic Journal of Combinatorics

    Authors : Thomas Selig ORCID, Jason P. Smith ORCID, Einar Steingrímsson ORCID

    Journal reference : Volume 25, 2018, pp.

    DOI : 10.37236/7480
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