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Literary linguistics: Open Access research in English language

Strathprints makes available Open Access scholarly outputs by English Studies at Strathclyde. Particular research specialisms include literary linguistics, the study of literary texts using techniques drawn from linguistics and cognitive science.

The team also demonstrates research expertise in Renaissance studies, researching Renaissance literature, the history of ideas and language and cultural history. English hosts the Centre for Literature, Culture & Place which explores literature and its relationships with geography, space, landscape, travel, architecture, and the environment.

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Crucial words for abelian powers

Glen, Amy and Halldorsson, Bjarni and Kitaev, Sergey (2009) Crucial words for abelian powers. In: Developments in Language Theory. Lecture Notes in Computer Science . Springer-Verlag Berlin, pp. 264-275. ISBN 978-3-642-02736-9

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Abstract

Let k ≥ 2 be an integer. An abelian k -th power is a word of the form X 1 X 2 ⋯ X k where X i is a permutation of X 1 for 2 ≤ i ≤ k. In this paper, we consider crucial words for abelian k-th powers, i.e., finite words that avoid abelian k-th powers, but which cannot be extended to the right by any letter of their own alphabets without creating an abelian k-th power. More specifically, we consider the problem of determining the minimal length of a crucial word avoiding abelian k-th powers. This problem has already been solved for abelian squares by Evdokimov and Kitaev [6], who showed that a minimal crucial word over an n-letter alphabet An={1,2,…,n} avoiding abelian squares has length 4n − 7 for n ≥ 3. Extending this result, we prove that a minimal crucial word over An avoiding abelian cubes has length 9n − 13 for n ≥ 5, and it has length 2, 5, 11, and 20 for n = 1,2,3, and 4, respectively. Moreover, for n ≥ 4 and k ≥ 2, we give a construction of length k 2(n − 1) − k − 1 of a crucial word over An avoiding abelian k-th powers. This construction gives the minimal length for k = 2 and k = 3.