Bounds on the frequency of 1 in the Kolakoski word

Details Bounds on the frequency of 1 in the Kolakoski word Bounds on the frequency of 1 in the Kolakoski word

2008-09-16

arxiv.org/abs/0809.2776v2

Mathematics

Combinatorics

6 pages, 1 figure; added reference to Chvatal's paper

Scientific paper

We use a method of Goulden and Jackson to bound freq_1(K), the limiting
frequency of 1 in the Kolakoski word K. We prove that |freq_1(K) - 1/2| <=
17/762, assuming the limit exists, and establish the semi-rigorous bound
|freq_1(K) - 1/2| <= 1/46.

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