Abstract | ||
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Let γ(n) be the number of C∞-words of length n. Say that a C∞-word w is left doubly extendable (LDE) if both 1w and 2w are C∞. We show that for any positive real number ϕ and positive integer N such that the proportion of 2’s is greater than 12−ϕ in each LDE word of length exceeding N, there are positive constants c1 and c2 such that c1nlog3log((3/2)+ϕ+(2/N))<γ(n)<c2nlog3log((3/2)−ϕ) for all positive integers n. With the best value known for ϕ, and large N, this gives c1n2.7087<γ(n)<c2n2.7102. |
Year | DOI | Venue |
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2010 | 10.1016/j.tcs.2010.06.024 | Theoretical Computer Science |
Keywords | DocType | Volume |
Kolakoski sequence,C∞-word | Journal | 411 |
Issue | ISSN | Citations |
40 | 0304-3975 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
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Yun Bao Huang | 1 | 0 | 1.01 |
William D. Weakley | 2 | 56 | 10.40 |