For any minimum piece size, the best decomposition of a word yields an eBWT with a bounded number of runs, while the worst decomposition yields the maximum possible number; the ratio is unbounded.
The Mahler measure of algebraic numbers: a survey
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A survey of results for Mahler measure of algebraic numbers, and one-variable polynomials with integer coefficients is presented. Related results on the maximum modulus of the conjugates (`house') of an algebraic integer are also discussed. Some generalisations are given too, though not to Mahler measure of polynomials in more than one variable.
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Decomposing Words for Enhanced Compression: Exploring the Number of Runs in the Extended Burrows-Wheeler Transform
For any minimum piece size, the best decomposition of a word yields an eBWT with a bounded number of runs, while the worst decomposition yields the maximum possible number; the ratio is unbounded.