Generating the Peano curve and counting occurrences of some patterns

Authors:
Sergey Kitaev;Toufik Mansour;Patrice Séébold
Affiliations:
Department of Mathematics, University of Kentucky, Lexington, KY;Department of Mathematics, Haifa University, Haifa, Israel;Université Paul Valéry - Montpellier, Montpellier Cedex, France and LaRIA, Université de Picardie Jules Verne, Amiens, France
Venue:
Journal of Automata, Languages and Combinatorics
Year:
2004

Citing 2
Cited 1

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Counting Ordered Patterns in Words Generated by Morphisms

Language and Automata Theory and Applications

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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.