Given a 0-1 sequence x in which both letters occur with density 1/2, do there exist arbitrarily long arithmetic progressions along which x reads 010101...? We answer the above negatively by showing that a certain regular triadic Toeplitz sequence does not have this property. On the other hand, we prove that if x is a generalized binary Morse sequence then each block can be read in x along some arithmetic progression.
@article{bwmeta1.element.bwnjournal-article-cmv80i2p293bwm,
author = {T. Downarowicz},
title = {Reading along arithmetic progressions},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {293-296},
zbl = {0940.11014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv80i2p293bwm}
}
Downarowicz, T. Reading along arithmetic progressions. Colloquium Mathematicae, Tome 79 (1999) pp. 293-296. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv80i2p293bwm/
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