Reading along arithmetic progressions

• Autorzy: T. Downarowicz
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Szemeredi Theorem; Morse sequence; Toeplitz sequence

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 80
• Numer: 2
• Strony: 293-296

Daty

wydano

1999

otrzymano

1998-12-10

poprawiono

1999-01-22

Twórcy

autor

T. Downarowicz

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

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