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Sub-word characterization of Kolakoski sequence

A word w in finite sequence of elements A∗ called letters and a sub-word of w contained in an infinite Kolakoski sequence K explained. An infinite Kolakoski sequence of word in various length |w| of the binary alphabet {1, 2} is partitioned as i blocks and j positions. Then for every positive intege...

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Bibliographic Details
Main Authors: Jansirani, N., Vigneswaran, L., Dare, V. R.
Format: Conference Proceeding
Language:English
Subjects:
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Summary:A word w in finite sequence of elements A∗ called letters and a sub-word of w contained in an infinite Kolakoski sequence K explained. An infinite Kolakoski sequence of word in various length |w| of the binary alphabet {1, 2} is partitioned as i blocks and j positions. Then for every positive integer n, the equivalence relation kn on A∗ is analyzed. In an infinite Kolakoksi sequence every Kolakoski word generates minimum of one and maximum of two sub-words δ {i, j} for every n ≥ 1 is shown. Also for every n the minimal and maximal distance of Kolakoski sub-words are increasing and decreasing respectively is established.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0156749