The minimal density of a letter in an infinite ternary square-free word is 0.2746 ...
Yuriy Valerievich Tarannikov · 2002
We study the minimal density of letters in inflnite square-free words. First, we give some deflnitions of minimal density in inflnite words and prove their equivalence. Further, we propose a method that allows to strongly reduce an exhaustive search for obtaining lower bounds for minimal density. Next, we develop a technique for constructing square-free morphisms with extremely small density for one letter that gives upper bounds on the minimal density. As an application of our technique we prove that the minimal density of any letter in inflnite ternary square-free words is 0:2746¢¢¢.