منابع مشابه
Ascending waves
A sequence of integers x, <x2 < < xk is called an ascending wave of length k if x~+~-x~<x~+~--~~+~ for all 1 < ig k-2. Let f(k) be the smallest positive integer such that any 2-coloring of { 1,2, . . . . f(k)} contains a monochromatic ascending wave of length k. Settling a problem of Brown, Erdiis, and Freedman we show that there are two positive constants c ,, c2 such that c,k3<f(k)<c2k3 for a...
متن کاملZero-Sum Ascending Waves
A sequence of positive integers a1 ≤ a2 ≤ . . . ≤ an is called an ascending monotone wave of length n, if ai+1−ai ≥ ai−ai−1 for i = 2, . . . , n−1. If ai+1−ai > ai−ai−1 for all i = 2, . . . , n−1 the sequence is called an ascending strong monotone wave of length n. Let Zk denote the cyclic group of order k. If k | n, then we define MW (n,Zk) as the least integer m such that for any coloring f :...
متن کاملOn Monochromatic Ascending Waves
A sequence of positive integers w1, w2, . . . , wn is called an ascending wave if wi+1 − wi ≥ wi − wi−1 for 2 ≤ i ≤ n − 1. For integers k, r ≥ 1, let AW (k; r) be the least positive integer such that under any r-coloring of [1, AW (k; r)] there exists a k-term monochromatic ascending wave. The existence of AW (k; r) is guaranteed by van der Waerden’s theorem on arithmetic progressions since an ...
متن کاملAsymptotic Stability of Ascending Solitary Magma Waves
Coherent structures, such as solitary waves, appear in many physical problems, including fluid mechanics, optics, quantum physics, and plasma physics. A less studied setting is found in geophysics, where highly viscous fluids couple to evolving material parameters to model partially molten rock, magma, in the Earth’s interior. Solitary waves are also found here, but the equations lack useful ma...
متن کاملOn the Asymptotic Behavior of Ascending Waves
Ramsey theory has been described in many ways. Weisteinn [1] defines Ramsey theory broadly as “the study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large.” It is the diversity of results considered to be those of Ramsey theory that requires this and any all-encompassing definition to be so vague. For this reason, Landman and Roberts...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1989
ISSN: 0097-3165
DOI: 10.1016/0097-3165(89)90033-2