Existence of arbitrarily long square-free words with one possible mismatch
Nikita Vladimirovich Kotlyarov · Discrete Mathematics and Applications · 2015
Abstract We are concerned with problems of the existence of periodic structures in words from formal languages. We consider both squares (that is, fragments of the form xx, where x is an arbitrary word) and squares with one mismatch (that is, fragments of the form xy, where a word x differs from a word y by exactly one letter). Given natural numbers l This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 14-01-00598) and of the Branch of Mathematics of the Russian Academy of Sciences Program “Algebraic and combinatorial methods of mathematical cybernetics and new generation information systems” (the project “Problem of optimal synthesis of control systems”).