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Gray code orders for \(q\)-ary words avoiding a given factor

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Abstract

Based on order relations inspired by the binary reflected Gray code (BRGC) we define Gray codes and give a generating algorithm for \(q\)-ary words avoiding a prescribed factor. These generalize an early 2001 result and a very recent one published by some of the present authors, and can be seen as an alternative to those of Squire published in 1996. Among the involved tools, we make use of generalized BRGC order relations, ultimate periodicity of infinite words, and word matching techniques.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica “Ulisse Dini”, Università degli Studi di Firenze, Viale G.B. Morgagni 65, 50134, Florence, Italy

    A. Bernini, S. Bilotta & R. Pinzani

  2. LE2I, Université de Bourgogne, BP 47 870, 21078, Dijon Cedex, France

    A. Sabri & V. Vajnovszki

Authors
  1. A. Bernini
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  2. S. Bilotta
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  3. R. Pinzani
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  4. A. Sabri
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  5. V. Vajnovszki
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Corresponding author

Correspondence to V. Vajnovszki.

Appendix

Appendix

See Tables 2 and 3.

Table 2 The set \(A_3^4\) listed in \(\triangleleft \) order, inducing a 2-Gray code
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Table 3 (a) The set \(A_2^4(011)\) listed in \(\prec \) order, inducing 3-adjacent Gray code; (b) the reverse of the list in (a), giving Gray code for \(A_2^4(110)\); (c) the complement of the list in (b), giving Gray code for \(A_2^4(001)\)
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Bernini, A., Bilotta, S., Pinzani, R. et al. Gray code orders for \(q\)-ary words avoiding a given factor. Acta Informatica 52, 573–592 (2015). https://doi.org/10.1007/s00236-015-0225-2

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  • DOI: https://doi.org/10.1007/s00236-015-0225-2

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