Bounds for the Kolakoski Sequence
نویسندگان
چکیده
The Kolakoski sequence (Kn) is perhaps one of the most famous examples of selfdescribing sequences for which some problems are still open. In particular, one does not know yet whether the density of 1’s in this sequence is equal to 12 . This work, which does not answer this question, provides explicit bounds for the main sequences related to (Kn). The proofs rest on a new identity involving the partial sums of (Kn) and on Dirichlet’s pigeonhole principle which allows us to improve notably on the error-term.
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