Reading along arithmetic progressions

Downarowicz, T.. "Reading along arithmetic progressions." Colloquium Mathematicae 80.2 (1999): 293-296. <http://eudml.org/doc/210719>.

@article{Downarowicz1999,
abstract = {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.},
author = {Downarowicz, T.},
journal = {Colloquium Mathematicae},
keywords = {Szemeredi Theorem; Morse sequence; Toeplitz sequence; arithmetic progressions},
language = {eng},
number = {2},
pages = {293-296},
title = {Reading along arithmetic progressions},
url = {http://eudml.org/doc/210719},
volume = {80},
year = {1999},
}

TY - JOUR
AU - Downarowicz, T.
TI - Reading along arithmetic progressions
JO - Colloquium Mathematicae
PY - 1999
VL - 80
IS - 2
SP - 293
EP - 296
AB - 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.
LA - eng
KW - Szemeredi Theorem; Morse sequence; Toeplitz sequence; arithmetic progressions
UR - http://eudml.org/doc/210719
ER -