On abelian versions of critical factorization theorem∗
1 Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
2 University of Turku, Department of Mathematics, 20014 Turku, Finland
3 Turku Centre for Computer Science, 20014 Turku, Finland
Received: 2 November 2010
Accepted: 2 August 2011
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.
Mathematics Subject Classification: 68R15
Key words: Combinatorics on words / periodicity / central factorization theorem / abelian properties of words.
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