Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.2

The minimal density of a letter in an infinite ternary square-free word is 0.2746 ...

Yuriy Tarannikov

Mech. and Math. Department
Moscow State University
119992 Moscow
Russia

Abstract: We study the minimal density of letters in infinite square-free words. First, we give some definitions of minimal density in infinite 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 infinite ternary square-free words is 0.2746 ... .

(Concerned with sequence A006156 .)

Received March 21, 2002; revised version received October 20, 2002. Published in Journal of Integer Sequences October 24, 2002.