Estimation of the number of aperiodic words
Автор: Senashov V.I.
Журнал: Siberian Aerospace Journal @vestnik-sibsau-en
Рубрика: Informatics, computer technology and management
Статья в выпуске: 3 vol.23, 2022 года.
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In 1902 W. Burnside raised the issue of local finiteness of groups, all elements of which are of finite order. The first negative answer was obtained in 1968 in the article by by P.S. Novikov and S.I. Adian. Finiteness of the free Burnside group of period n was established for n = 2, n = 3 (W. Burnside), n = 4 (W. Burnside, I. N. Sanov), n = 6 (M. Hall). The proof of infinity of this group for odd n ≥ 4381 was given in the article by P. S. Novikov and S. I. Adian (1967); for odd n ≥ 665 in the monograph by S. I. Adian (1975). In relation with these results we consider the set of m-aperiodic words. Word is called l-aperiodic if there are no non-empty subwords of the form Yl in it. In the monograph by S. I. Adian (1975) the proof of S. E. Arshon (1937) of the fact that in the two-letters alphabet there is an infinite set of arbitrarily long 3-aperiodic words was shown. In the A.Yu. Olshansky’s monograph (1989) the theorem on the infinity of the set of 6-aperiodic words was proved, and a lower bound function for the number of words of a given length was obtained. Our aim is to get an estimate for the function ()fn of the number of m-aperiodic words of the length n in the two-letters alphabet. The results can be applied when encoding information in space communications.
Group, periodic word, aperiodic word, alphabet, local finiteness
Короткий адрес: https://sciup.org/148329637
IDR: 148329637 | DOI: 10.31772/2712-8970-2022-23-3-409-416
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