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The paper is concerned with the problem of existence of periodic structures in words from formal languages. Squares (that is, fragments of the form  xx , where  x  is an arbitrary word) and  Δ -squares (that is, fragments of the form  xy , where a word  x  differs from a word  y  by at most  Δ  letters) are considered as periodic structures. We show that in a binary alphabet there exist arbitrarily long words free from  Δ -squares with length at most 4 Δ +4. In particular, a method of construction of such words for any  Δ  is given.

Existence of words over a binary alphabet free from squares with mismatches