Equations in the Partial Semigroup of Words with Overlapping Products

We consider an overlapping product of words as a partial operation where the product of two words is defined when the former ends with the same letter as the latter starts, and in this case the product is obtained by merging these two occurrences of letters, for example aba ∙ ab = abab. Some basic results on equations of words are established by reducing them to corresponding results of ordinary word equations.

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