1. AVOIDING MONOCHROMATIC SEQUENCES WITH SPECIAL GAPS.
- Author
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Landman, Bruce M. and Robertson, Aaron
- Subjects
- *
ARITHMETIC series , *ARITHMETIC , *RAMSEY theory , *COLOR blindness , *MATHEMATICAL series - Abstract
For S ⊆ℤ+ and k and r fixed positive integers, denote by f(S, k; r) the least positive integer n (if it exists) such that within every r-coloring of {1, 2,…,n} there must be a monochromatic sequence {x1,x2,…,xκ} with xi - xi-1 ∈ S for 2 ≤ ≤ κ. We consider the existence of f(S, k; r) for various choices of S, as well as upper and lower bounds on this function. In particular, we show that this function exists for all k if S is an odd translate of the set of primes and r =2. [ABSTRACT FROM AUTHOR]
- Published
- 2007
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