An analysis of words coming from Chacon's transformation
Abstract
We analyze finite and infinite words coming from the symbolic version of Chacon's transformation, focusing on distances between such words. Our main result is that if W = 0010 0010 1 0010 ... is the infinite word usually associated with Chacon's transformation, then the Hamming distance between W and any positive shift of W is strictly greater than 2/9; moreover, this bound is sharp. This yields an alternate proof that Chacon's transformation is non-rigid and (using King's weak closure theorem) has trivial centralizer.
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