Binary words are conjectured to contain at least floor(n/4) abelian squares, with the bound proven in special cases and candidate minimal words constructed for every Parikh vector.
On The Minimum Number of Abelian Squares in a Word Combinatorics and Algorithmics of Strings , Dagstuhl Reports, 4(2014), Issue 3, 34-35
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Binary Words Containing Few Abelian Squares
Binary words are conjectured to contain at least floor(n/4) abelian squares, with the bound proven in special cases and candidate minimal words constructed for every Parikh vector.