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On Avoiding Sufficiently Long Abelian Squares
A finite word is an abelian square if with a
permutation of . In 1972, Entringer, Jackson, and Schatz proved that every
binary word of length contains an abelian square of length . We use Cartesian lattice paths to characterize abelian squares in binary
sequences, and construct a binary word of length avoiding abelian
squares of length or greater. We thus prove that the
length of the longest binary word avoiding abelian squares of length is
.Comment: 5 page