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Sets of integers avoiding congruent subsets

✍ Scribed by Tesoro, Rafael

Book ID: 122575642
Publisher: Elsevier Science
Year: 2013
Tongue: English
Weight: 155 KB
Volume: 43
Category: Article
ISSN: 1571-0653
DOI: 10.1016/j.endm.2013.07.023

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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