منابع مشابه
Disjunctive Rado numbers
If L1 and L2 are linear equations, then the disjunctive Rado number of the set {L1, L2} is the least integer n, provided that it exists, such that for every 2-coloring of the set {1, 2, . . . , n} there exists a monochromatic solution to either L1 or L2. If such an integer n does not exist, then the disjunctive Rado number is infinite. In this paper, it is shown that for all integers a 1 and b ...
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In this paper new proofs of the Canonical Ramsey Theorem, which originally has been proved by ErdSs and Rado, are given. These yield improvements over the known bounds for the arising Erd6s-Rado numbers ER(k; l), where the numbers ER(k; l) are defined as the least positive integer n such that for every partition of the k-element subsets of a totally ordered n-element set X into an arbitrary num...
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This was first proven by van der Warden [6]. See the books by Graham, Rothchild, and Spencer [3], Landman and Robertson [4] or the free on-line book of Gasarch, Kruskal, Parrish [1] for the proof in English. This proof gives enormous upper bounds on the numbers W (k, c) that are not primitive recursive. Shelah [5] gave an alternative proof that yields primitive recursive upper bounds. All of th...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2003
ISSN: 0196-8858
DOI: 10.1016/s0196-8858(03)00020-4