Abstract
We will prove that the word \(a^ib^ja^k\) is periodicity forcing if \(j \ge 3\) and \(i+k \ge 3\), where \(i\) and \(k\) are positive integers. Also we will give examples showing that both bounds are optimal.
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References
Barbin-Le Rest, E., Le Rest, M.: Sur la combinatoire des codes à deux mots. Theor. Comput. Sci. 41, 61–80 (1985)
Culik II, K., Karhumäki, J.: On the equality sets for homomorphisms on free monoids with two generators. RAIRO ITA 14(4), 349–369 (1980)
Czeizler, E., Holub, Š., Karhumäki, J., Laine, M.: Intricacies of simple word equations: an example. Internat. J. Found. Comput. Sci. 18(6), 1167–1175 (2007)
Lentin, A., Schützenberger, M.-P.: A combinatorial problem in the theory of free monoids. In: Pollak, G. (ed.) Algebraic Theory of Semigroups. North-Holland Pub. Co, Amsterdam (1979)
Lyndon, R.C., Schützenberger, M.-P.: The equation \(a^m=b^nc^p\) in a free group. The Michigan Mathematical Journal 9(4), 289–298 (1962)
Rozenberg, G., Salomaa, A. (eds.): Handbook of formal languages, vol. 1: word, language, grammar. Springer-Verlag New York Inc., USA (1997)
Spehner, J.-C.: Quelques problèmes d’extension, de conjugaison et de presentation des sous-monoïdes d’un monoïde libre. Ph.D. thesis, Université Paris VII, Paris (1976)
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Hadravová, J., Holub, Š. (2015). Equation \(x^iy^jx^k=u^iv^ju^k\) in Words. In: Dediu, AH., Formenti, E., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2015. Lecture Notes in Computer Science(), vol 8977. Springer, Cham. https://doi.org/10.1007/978-3-319-15579-1_32
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DOI: https://doi.org/10.1007/978-3-319-15579-1_32
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