Toeplitz words, generalized periodicity and periodically iterated morphisms
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We consider so-called Toeplitz words which can be viewed as generalizations of one-way infinite periodic words. We compute their subword complexity, and show that they can always be generated by iterating periodically a finite number of morphisms. Moreover, we define a structural classification of Toeplitz words which is reflected in the way how they can be generated by iterated morphisms.
KeywordsFinite Alphabet Generalize Periodicity Consecutive Block Periodic Iteration Infinite Word
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- 1.J.-P. Allouche, Sur la complexité des suites infinies, Bull. Belg. Math. Soc.1 (1994), 133–143.Google Scholar
- 2.J.-P. Allouche and R. Bacher, Toeplitz sequences, paperfolding, towers of Hanoi and progression free sequences of integers, Ens. Math.38 (1992), 315–327.Google Scholar
- 3.K. Culik II, J. Karhumäki, and A. Lepistö, Alternating iteration of morphisms and the Kolakoski sequence, in Lindenmayer systems, G. Rozenberg and A. Salomaa, eds., pp. 93–106, Springer-Verlag, 1992.Google Scholar
- 4.C. Davis and D. E. Knuth, Number representations and dragon curves I, II, J. Recr. Math.3 (1970), 61–81 and 133–149.Google Scholar
- 6.N. J. Fine and H. S. Wilf, Uniqueness theorem for periodic functions, Proc. Am. Math. Soc.16 (1965), 109–114.Google Scholar
- 7.H. Furstenberg, Recurrences in ergodic theory and combinatorial number theory, Princeton Univ. Press, 1981.Google Scholar
- 10.A. Lepistö, On the power of periodic iteration of morphisms, in ICALP '93, pp. 496–506, Lect. Notes Comput. Sci. 700, Springer-Verlag, 1993.Google Scholar
- 11.M. Lothaire, Combinatorics on Words, vol. 17 of Encyclopedia of Mathematics and its Applications, Addison-Wesley, 1983.Google Scholar
- 12.M. Mendès France and A. J. van der Poorten, Arithmetic and analytic properties of paperfolding sequences, Bull. Austr. Math. Soc. 24 (1981).Google Scholar