On Avoiding Sufficiently Long Abelian Squares
نویسنده
چکیده
A finite word w is an abelian square if w = xx′ with x′ a permutation of x. In 1972, Entringer, Jackson, and Schatz proved that every binary word of length k2+6k contains an abelian square of length ≥ 2k. We use Cartesian lattice paths to characterize abelian squares in binary sequences, and construct a binary word of length q(q + 1) avoiding abelian squares of length ≥ 2 √ 2q(q + 1) or greater. We thus prove that the length of the longest binary word avoiding abelian squares of length 2k is Θ(k2).
منابع مشابه
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عنوان ژورنال:
- CoRR
دوره abs/1012.0524 شماره
صفحات -
تاریخ انتشار 2010