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Generating the Peano curve and counting occurrences of some patterns

Kitaev, Sergey and Mansour, Toufik and Seebold, Patrice (2004) Generating the Peano curve and counting occurrences of some patterns. Journal of Automata, Languages and Combinatorics, 9 (4). pp. 439-455.

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Abstract

We introduce Peano words, which are words corresponding to finite approximations of the Peano space filling curve. We find the number of occurrences of certain patterns in these words. We give a tag-system to generate automatically these words and, by showing that they are almost cube-free, we prove that they cannot be obtained by simply iterating a morphism.