Geodesic
Reading along arithmetic progressions
Colloquium Mathematicum, Tome 80 (1999) no. 2, pp. 293-296

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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.
DOI : 10.4064/cm-80-2-293-296
Keywords: Szemeredi Theorem, Morse sequence, Toeplitz sequence

T. Downarowicz 1

1 
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T. Downarowicz. Reading along arithmetic progressions. Colloquium Mathematicum, Tome 80 (1999) no. 2, pp. 293-296. doi: 10.4064/cm-80-2-293-296

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