On abelian versions of critical factorization theorem

Sergey Avgustinovich; Juhani Karhumäki; Svetlana Puzynina

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2012)

  • Volume: 46, Issue: 1, page 3-15
  • ISSN: 0988-3754

Abstract

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In the paper 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.

How to cite

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Avgustinovich, Sergey, Karhumäki, Juhani, and Puzynina, Svetlana. "On abelian versions of critical factorization theorem." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 46.1 (2012): 3-15. <http://eudml.org/doc/273045>.

@article{Avgustinovich2012,
abstract = {In the paper 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.},
author = {Avgustinovich, Sergey, Karhumäki, Juhani, Puzynina, Svetlana},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {combinatorics on words; periodicity; central factorization theorem; abelian properties of words},
language = {eng},
number = {1},
pages = {3-15},
publisher = {EDP-Sciences},
title = {On abelian versions of critical factorization theorem},
url = {http://eudml.org/doc/273045},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Avgustinovich, Sergey
AU - Karhumäki, Juhani
AU - Puzynina, Svetlana
TI - On abelian versions of critical factorization theorem
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2012
PB - EDP-Sciences
VL - 46
IS - 1
SP - 3
EP - 15
AB - In the paper 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.
LA - eng
KW - combinatorics on words; periodicity; central factorization theorem; abelian properties of words
UR - http://eudml.org/doc/273045
ER -

References

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  1. [1] S.V. Avgustinovich and A.E. Frid, Words avoiding abelian inclusions. J. Autom. Lang. Comb.7 (2002) 3–9. Zbl1021.68069MR1915289
  2. [2] Y. Césari and M. Vincent, Une caractérisation des mots périodiques. C.R. Acad. Sci. Paris, Ser. A 286 (1978) 1175–1177. Zbl0392.20039
  3. [3] J. Cassaigne and J. Karhumäki, Toeplitz words, generalized periodicity and periodically iterated morphisms. Eur. J. Comb.18 (1997) 497–510. Zbl0881.68065MR1455183
  4. [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. Zbl1223.68089MR2806895
  5. [5] J.-P. Duval, Périodes et répetitions des mots du monoide libre. Theoret. Comput. Sci.9 (1979) 17–26. Zbl0402.68052MR535121
  6. [6] J. Karhumäki, A. Lepistö and W. Plandowski, Locally periodic versus globally periodic infinite words. J. Comb. Th. (A) 100 (2002) 250–264. Zbl1011.68070MR1940335
  7. [7] A. Lepistö, On Relations between Local and Global Periodicity. Ph.D. thesis (2002). Zbl0941.68658
  8. [8] M. Lothaire, Algebraic combinatorics on words. Cambridge University Press (2002). Zbl1221.68183MR1905123
  9. [9] F. Mignosi, A. Restivo and S. Salemi, Periodicity and the golden ratio. Theoret. Comput. Sci.204 (1998) 153–167. Zbl0913.68162MR1637524
  10. [10] G. Richomme, K. Saari and L. Zamboni, Abelian complexity of minimal subshifts. J. London Math. Soc.83 (2011) 79–95. Zbl1211.68300MR2763945
  11. [11] K. Saari, Everywhere α-repetitive sequences and Sturmian words. Eur. J. Comb.31 (2010) 177–192. Zbl1187.68369MR2552600
  12. [12] O. Toeplitz, Beispiele zur theorie der fastperiodischen Funktionen. Math. Ann.98 (1928) 281–295. Zbl53.0241.02MR1512405JFM53.0241.02

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