Abstract
A set A⊆N is called sparse if, for some N0, the distance between any two elements of A is at least N0. James Currie (2008) [2] showed that for each sparse set A and every subset P⊆A there exists a ternary square-free word wP such that a palindrome of length three starts at position i∈A in wP if and only if i∈P. We provide a simpler proof of this result that also works for shorter distances between the positions.
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