Geodesic
A one-sided Zimin construction
The electronic journal of combinatorics, Tome 8 (2001) no. 1
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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.
DOI : 10.37236/1571
Classification : 68R15, 20M35
Mots-clés : Abelian square-free string 
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     author = {L. J. Cummings and M. Mays},
     title = {A one-sided {Zimin} construction},
     journal = {The electronic journal of combinatorics},
     year = {2001},
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     number = {1},
     doi = {10.37236/1571},
     zbl = {0969.68120},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1571/}
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L. J. Cummings; M. Mays. A one-sided Zimin construction. The electronic journal of combinatorics, Tome 8 (2001) no. 1. doi: 10.37236/1571

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