Cummings, L. J.; Mays, M. A one-sided Zimin construction. (English) Zbl 0969.68120 Electron. J. Comb. 8, No. 1, Research paper R27, 9 p. (2001). Summary: A string is Abelian square-free if it contains no Abelian squares; that is, adjacent substrings which are permutations of each other. An Abelian square-free string is maximal if it cannot be extended to the left or right by concatenating alphabet symbols without introducing an Abelian square. We construct Abelian square-free finite strings which are maximal by modifying a construction of Zimin. The new construction produces maximal strings whose length as a function of alphabet size is much shorter than that in the construction described by Zimin. Cited in 3 Documents MSC: 68R15 Combinatorics on words 20M35 Semigroups in automata theory, linguistics, etc. Keywords:Abelian square-free string PDFBibTeX XMLCite \textit{L. J. Cummings} and \textit{M. Mays}, Electron. J. Comb. 8, No. 1, Research paper R27, 9 p. (2001; Zbl 0969.68120) Full Text: EuDML EMIS Online Encyclopedia of Integer Sequences: Concatenation of terms of A018238. Length of the n-th Zimin word (A082215(n)).