On abelian versions of critical factorization theorem. (English) Zbl 1247.68200

Summary: We study abelian versions of the critical factorization theorem. We investigate both similarities and differences between the abelian powers and the usual powers. The results we obtained show that the constraints for abelian powers implying periodicity should be quite strong, but still natural analogies exist.


68R15 Combinatorics on words
Full Text: DOI EuDML Link


[1] S.V. Avgustinovich and A.E. Frid, Words avoiding abelian inclusions. J. Autom. Lang. Comb.7 (2002) 3-9. · Zbl 1021.68069
[2] Y. Césari and M. Vincent, Une caractérisation des mots périodiques. C.R. Acad. Sci. Paris, Ser. A286 (1978) 1175-1177. · Zbl 0392.20039
[3] J. Cassaigne and J. Karhumäki, Toeplitz words, generalized periodicity and periodically iterated morphisms. Eur. J. Comb.18 (1997) 497-510. · Zbl 0881.68065
[4] J. Cassaigne, G. Richomme, K. Saari and L.Q. Zamboni, Avoiding Abelian powers in binary words with bounded Abelian complexity. Int. J. Found. Comput. Sci.22 (2011) 905-920. · Zbl 1223.68089
[5] J.-P. Duval, Périodes et répetitions des mots du monoide libre. Theoret. Comput. Sci.9 (1979) 17-26. Zbl0402.68052 · Zbl 0402.68052
[6] J. Karhumäki, A. Lepistö and W. Plandowski, Locally periodic versus globally periodic infinite words. J. Comb. Th. (A)100 (2002) 250-264. · Zbl 1011.68070
[7] A. Lepistö, On Relations between Local and Global Periodicity. Ph.D. thesis (2002).
[8] M. Lothaire, Algebraic combinatorics on words. Cambridge University Press (2002). · Zbl 1001.68093
[9] F. Mignosi, A. Restivo and S. Salemi, Periodicity and the golden ratio. Theoret. Comput. Sci.204 (1998) 153-167. · Zbl 0913.68162
[10] G. Richomme, K. Saari and L. Zamboni, Abelian complexity of minimal subshifts. J. London Math. Soc.83 (2011) 79-95. Zbl1211.68300 · Zbl 1211.68300
[11] K. Saari, Everywhere \alpha -repetitive sequences and Sturmian words. Eur. J. Comb.31 (2010) 177-192. Zbl1187.68369 · Zbl 1187.68369
[12] O. Toeplitz, Beispiele zur theorie der fastperiodischen Funktionen. Math. Ann.98 (1928) 281-295. · JFM 53.0241.02
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.