Chip-Firing And A Devil's Staircase
2009 ◽
Vol DMTCS Proceedings vol. AK,...
(Proceedings)
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Keyword(s):
International audience 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.
1983 ◽
Vol 50
(21)
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pp. 1637-1639
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1994 ◽
Vol 115
(3)
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pp. 451-481
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1985 ◽
Vol 46
(7)
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pp. 1205-1209
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1984 ◽
Vol 52
(6)
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pp. 480-480
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1997 ◽
Vol 231
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pp. 152-158
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2000 ◽
Vol 50
(3)
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pp. 307-311
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2018 ◽
Vol 2018
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