Lionel Levine - Chip-Firing And A Devil's Staircase

dmtcs:2693 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2693
Chip-Firing And A Devil's StaircaseArticle

Authors: Lionel Levine ORCID1

  • 1 Department of Mathematics [MIT]

The devil's staircase ― a continuous function on the unit interval $[0,1]$ which is not constant, yet is locally constant on an open dense set ― is the sort of exotic creature a combinatorialist might never expect to encounter in "real life.'' We show how a devil's staircase arises from the combinatorial problem of parallel chip-firing on the complete graph. This staircase helps explain a previously observed "mode locking'' phenomenon, as well as the surprising tendency of parallel chip-firing to find periodic states of small period.


Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: Circle map,fixed-energy sandpile,mode locking,non-ergodicity,parallel chip-firing,rotation number,short period attractors,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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