Claims

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1957_11_16_de_bruijn_erdos: Erdős reports in 1957 and 1961 that he and de Bruijn disproved at k = 4 his conjecture that every string of length 2^k over k symbols, printed as 2^k - 1, has an abelian square; no construction is given.

1992_07_13_keranen: Keränen's 85-uniform morphism gives an infinite word over four letters with no abelian square, so for every k at least 4 a string of length 2^k over k letters can avoid abelian squares; credited by the site's curator.

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