Words avoiding repetitions in arithmetic progressions
组合数学
2007-05-23 v2
摘要
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 arbitrarily 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.
引用
@article{arxiv.math/0608607,
title = {Words avoiding repetitions in arithmetic progressions},
author = {Jui-Yi Kao and Narad Rampersad and Jeffrey Shallit and Manuel Silva},
journal= {arXiv preprint arXiv:math/0608607},
year = {2007}
}
备注
18 pages; Manuel Silva added as a co-author