On abelian versions of critical factorization theorem∗
Sergey Avgustinovich; Juhani Karhumäki; Svetlana Puzynina
RAIRO - Theoretical Informatics and Applications (2012)
- Volume: 46, Issue: 1, page 3-15
- ISSN: 0988-3754
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topAvgustinovich, Sergey, Karhumäki, Juhani, and Puzynina, Svetlana. "On abelian versions of critical factorization theorem∗." RAIRO - Theoretical Informatics and Applications 46.1 (2012): 3-15. <http://eudml.org/doc/222029>.
@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},
keywords = {Combinatorics on words; periodicity; central factorization theorem; abelian properties of words.; combinatorics on words; abelian properties of words},
language = {eng},
month = {3},
number = {1},
pages = {3-15},
publisher = {EDP Sciences},
title = {On abelian versions of critical factorization theorem∗},
url = {http://eudml.org/doc/222029},
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
DA - 2012/3//
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.; combinatorics on words; abelian properties of words
UR - http://eudml.org/doc/222029
ER -
References
top- S.V. Avgustinovich and A.E. Frid, Words avoiding abelian inclusions. J. Autom. Lang. Comb.7 (2002) 3–9.
- Y. Césari and M. Vincent, Une caractérisation des mots périodiques. C.R. Acad. Sci. Paris, Ser. A286 (1978) 1175–1177.
- J. Cassaigne and J. Karhumäki, Toeplitz words, generalized periodicity and periodically iterated morphisms. Eur. J. Comb.18 (1997) 497–510.
- 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.
- J.-P. Duval, Périodes et répetitions des mots du monoide libre. Theoret. Comput. Sci.9 (1979) 17–26.
- J. Karhumäki, A. Lepistö and W. Plandowski, Locally periodic versus globally periodic infinite words. J. Comb. Th. (A)100 (2002) 250–264.
- A. Lepistö, On Relations between Local and Global Periodicity. Ph.D. thesis (2002).
- M. Lothaire, Algebraic combinatorics on words. Cambridge University Press (2002).
- F. Mignosi, A. Restivo and S. Salemi, Periodicity and the golden ratio. Theoret. Comput. Sci.204 (1998) 153–167.
- G. Richomme, K. Saari and L. Zamboni, Abelian complexity of minimal subshifts. J. London Math. Soc.83 (2011) 79–95.
- K. Saari, Everywhere α-repetitive sequences and Sturmian words. Eur. J. Comb.31 (2010) 177–192.
- O. Toeplitz, Beispiele zur theorie der fastperiodischen Funktionen. Math. Ann.98 (1928) 281–295.
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