Kolakoski sequence: links between recurrence, symmetry and limit density
2021 ◽
Vol 4
(1)
◽
pp. 29-44
Keyword(s):
The Kolakoski sequence $S$ is the unique element of \(\left\lbrace 1,2 \right\rbrace^{\omega}\) starting with 1 and coinciding with its own run length encoding. We use the parity of the lengths of particular subclasses of initial words of \(S\) as a unifying tool to address the links between the main open questions - recurrence, mirror/reversal invariance and asymptotic density of digits. In particular we prove that recurrence implies reversal invariance, and give sufficient conditions which would imply that the density of 1s is \(\frac{1}{2}\).
1986 ◽
Vol 9
(4)
◽
pp. 801-806
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2015 ◽
Vol 30
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pp. 530-549
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Keyword(s):
1999 ◽
Vol 42
(1)
◽
pp. 25-36
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2004 ◽
Vol 2004
(6)
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pp. 461-470
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2009 ◽
Vol 02
(02)
◽
pp. 295-305
1986 ◽
Vol 23
(04)
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pp. 851-858
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2011 ◽
Vol 23
(1)
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pp. 60-63
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