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Avoiding cross-bifix-free binary words

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Abstract

In this paper we study the construction and the enumeration of binary words in \(\{0,1\}^*\) having more 1’s than 0’s and avoiding a set of cross-bifix-free patterns. We give a particular succession rule, called jumping and marked succession rule, which describes the growth of such words according to their number of ones. Moreover, the problem of associating a word to a path in the generating tree obtained by the succession rule is solved by introducing an algorithm which constructs all binary words having more 1’s than 0’s and then kills those containing the forbidden patterns. Finally, we give the generating function of such words according to the number of ones.

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Authors and Affiliations

  1. Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Viale G.B. Morgagni 65, 50134,  Firenze, Italy

    Stefano Bilotta, Elisabetta Grazzini, Elisa Pergola & Renzo Pinzani

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  1. Stefano Bilotta
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  2. Elisabetta Grazzini
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  3. Elisa Pergola
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  4. Renzo Pinzani
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Correspondence to Elisabetta Grazzini.

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Bilotta, S., Grazzini, E., Pergola, E. et al. Avoiding cross-bifix-free binary words. Acta Informatica 50, 157–173 (2013). https://doi.org/10.1007/s00236-013-0176-4

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  • DOI: https://doi.org/10.1007/s00236-013-0176-4

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