Abstract
Given a binary word that contains two (not necessarily disjont) subpalindromes whose total length is large enough (in a certain sense), we show an upper bound (less than 1) on the ratio between the number of occurrences of its less frequent letter and its more frequent letter. This theorem was a key step in a recent article on the so-called MP-ratio, and here it is proved by a different approach, one that provides a deeper insight into the essence of what makes the theorem true. Additionally, we show that the presented bound is tight, and give an explicit description of all the cases when the equality is reached.
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