Natural bijections for contiguous pattern avoidance in words

12/17/2022

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by   Julia Carrigan, et al.

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Two words p and q are avoided by the same number of length-n words, for all n, precisely when p and q have the same set of border lengths. However, known proofs of this result use generating functions and do not provide explicit bijections. We establish a natural bijection from the set of words avoiding p to the set of words avoiding q in the case that p and q have the same set of proper borders.