Words avoiding repetitions in arithmetic progressions

Authors:
Jui-Yi Kao;Narad Rampersad;Jeffrey Shallit;Manuel Silva
Affiliations:
David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada;David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada;David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada;Departamento de Matemática, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal
Venue:
Theoretical Computer Science
Year:
2008

Citing 2
Cited 1

Multidimensional unrepetitive configurations (note)

Theoretical Computer Science
Canonical positions for the factors in paperfolding sequences

Theoretical Computer Science

Abelian powers in paper-folding words

Journal of Combinatorial Theory Series A

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Abstract

Carpi constructed an infinite word over a 4-letter alphabet that avoids squares in all subsequences indexed by arithmetic progressions of odd difference. We show a connection between Carpi's construction and the paperfolding words. We extend Carpi's result by constructing uncountably many words that avoid squares in arithmetic progressions of odd difference. We also construct infinite words avoiding overlaps and infinite words avoiding all sufficiently large squares in arithmetic progressions of odd difference. We use these words to construct labelings of the 2-dimensional integer lattice such that any line through the lattice encounters a squarefree (resp. overlapfree) sequence of labels.