On a Variant of Van Der Waerden’s Theorem
نویسنده
چکیده
Given positive integers n and k, a k-term quasi-progression of diameter n is a sequence (x1, x2, ..., xk) such that d ≤ xj+1−xj ≤ d+n, 1 ≤ j ≤ k−1, for some positive integer d. Thus an arithmetic progression is a quasi-progression of diameter 0. Let Qn(k) denote the least integer for which every coloring of {1, 2, ..., Qn(k)} yields a monochromatic k-term quasi-progression of diameter n. We obtain an exponential lower bound on Q1(k) using probabilistic techniques and linear algebra.
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تاریخ انتشار 2010