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Ramsey–Sperner theory

✍ Scribed by Zoltán Füredi; Jerrold R. Griggs; Andrew M. Odlyzko; James B. Shearer

Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
667 KB
Volume
63
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

Let [n] denote the n-set {1,2, . . . , n}, let k, 12 1 be integers. Define fi(n, k) as the minimum number f such that for every family F c 2'"' with (F( > f, for every k-coloring of [n], there exists a chain A, E. . . f Al+, in F in which the set of added elements, AI+l-A1, is monochromatic.

We survey the known results for 1 = 1. Applying them we prove for any fixed 1 that there exists a constant q+(k) such that as n --, 00 h(n. k) -W)( [in,) and v,(k) -1 G as k-t m.

Several problems remain open.

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