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A note on the intersection properties of subsets of integers

✍ Scribed by R.L Graham; M Simonovits; V.T Sós

Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
229 KB
Volume
28
Category
Article
ISSN
0097-3165

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📜 SIMILAR VOLUMES

Intersection Properties of Subsets of In
Intersection Properties of Subsets of Integers
✍ Tibor Szabó 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 241 KB

Let N k be the maximal integer such that there exist subsets A 1 , . . . , A N k ⊆ {1, 2, . . . , n} for which A i ∩ A j is an arithmetic progression of length at least k for every 1 ≤ i < j ≤ N k . Graham, Simonovits and Sós gave the exact value of N 0 . For k ≥ 2, Simonovits and Sós determined the

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✍ Ronald Graham; Vojtech Rödl; Andrzej Ruciński 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 792 KB

A classic result of I. Schur [9] asserts that for every r 2 and for n sufficiently large, if the set [n]=[1, 2, ..., n] is partitioned into r classes, then at least one of the classes contains a solution to the equation x+ y=z. Any such solution with x{y will be called a Schur triple. Let us say tha