# Reading along arithmetic progressions

Colloquium Mathematicae (1999)

- Volume: 80, Issue: 2, page 293-296
- ISSN: 0010-1354

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topDownarowicz, 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 -

## References

top- [F] H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton Univ. Press, Princeton, N.J., 1981. Zbl0459.28023
- [W] S. Williams, Toeplitz minimal flows which are not uniquely ergodic, Z. Wahrsch. Verw. Gebiete 67 (1984), 95-107. Zbl0584.28007

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