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Specifying periodic words by restrictions

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Abstract

Consider a periodic sequence over a finite alphabet, say ..ababab.... This sequence can be specified by prohibiting the subwords aa and bb. In the paper, the maximum period of a word that can be defined by using k restrictions is determined. A sharp exponential bound is obtained: the period of a word determined by k restrictions cannot exceed the kth Fibonacci number. Thus, the period colength is estimated. The problem is studied in the context of Gröbner bases, namely, the growth of a Gröbner basis of an ideal (the cogrowth of an algebra). The proof uses the technique of Rauzy graphs.

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Authors and Affiliations

  1. Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991, Russia

    P. A. Lavrov

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  1. P. A. Lavrov
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Correspondence to P. A. Lavrov.

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Original Russian Text © P.A. Lavrov, 2016, published in Doklady Akademii Nauk, 2016, Vol. 468, No. 5, pp. 492–495.

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Lavrov, P.A. Specifying periodic words by restrictions. Dokl. Math. 93, 300–303 (2016). https://doi.org/10.1134/S1064562416030224

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  • DOI: https://doi.org/10.1134/S1064562416030224

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