M-aperiodic words on three-letter alphabet

Asymmetric repetition-free sequence for an alphabet of at least three letters. In the monograph by S.I. Adyan proved that in an alphabet of two symbols there exist infinite 3-aperiodic sequences. In the works of other authors, generalizations of aperiodicity were considered, when not only the powers of some subwords were excluded. In the monograph by A.Yu. Olshansky proved the infinity of the set of 6-aperiodic words in a two-letter alphabet and obtained an estimate for the number of such words of any given length. The author previously considered the case of a three-letter alphabet only in the case of 6-aperiodic words. In this article, we prove the infinity of the set of m-aperiodic words in the three-letter alphabet at m ³ 4 and obtain an estimate for the set of such words. The results can be applied when encoding information in space communications.