# Logarithmic equal-letter runs for BWT of purely morphic words

In this paper we study the number r_bwt of equal-letter runs produced by the Burrows-Wheeler transform (BWT) when it is applied to purely morphic finite words, which are words generated by iterating prolongable morphisms. Such a parameter r_bwt is very significant since it provides a measure of the performances of the BWT, in terms of both compressibility and indexing. In particular, we prove that, when BWT is applied to any purely morphic finite word on a binary alphabet, r_bwt is 𝒪(log n), where n is the length of the word. Moreover, we prove that r_bwt is Θ(log n) for the binary words generated by a large class of prolongable binary morphisms. These bounds are proved by providing some new structural properties of the bispecial circular factors of such words.

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