Geodesic
Existence of words over a three-letter alphabet not containing squares with errors of replacing
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2018), pp. 8-16

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The paper concerns some problems related to the existence of periodic structures in words from formal languages. Squares, i.e. fragments of the form $xx$, where $x$ is some word, and $\Delta$-squares, i.e. fragments of the form $xy$, where the word $x$ is different from the word $y$ by not more than $\Delta$ letters, are considered as periodic structures. We show the existence of arbitrarily long words over three-letter alphabet not containing $\Delta$-squares with the period exceeding $\Delta$. In particular, such words are constructed for all possible values $\Delta$. 
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     author = {N. V. Kotlyarov},
     title = {Existence of words over a three-letter alphabet not containing squares with errors of replacing},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {8--16},
     publisher = {mathdoc},
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     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2018_3_a1/}
}
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N. V. Kotlyarov. Existence of words over a three-letter alphabet not containing squares with errors of replacing. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2018), pp. 8-16. http://geodesic.mathdoc.fr/item/VMUMM_2018_3_a1/