Bounds on the frequency of 1 in the Kolakoski word
Abstract
We use a method of Goulden and Jackson to bound freq1(K), the limiting frequency of 1 in the Kolakoski word K. We prove that |freq1(K) - 1/2| <= 17/762, assuming the limit exists, and establish the semi-rigorous bound |freq1(K) - 1/2| <= 1/46.
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