The size of Higman–Haines sets
نویسندگان
چکیده
منابع مشابه
The Size of Sets With
Let n be a nonzero integer and a1 < a2 < · · · < am positive integers such that aiaj + n is a perfect square for all 1 ≤ i < j ≤ m. It is known that m ≤ 5 for n = 1. In this paper we prove that m ≤ 31 for |n| ≤ 400 and m < 15.034 log |n| for |n| > 400.
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In fact, this statement is a corollary to a more general theorem on well-partiallyordered sets. Here a partially ordered set is called well-partially-ordered, if every non-empty subset has at least one, but no more than a finite number of minimal elements (finite basis property). For instance, the set A∗, where A is a finite alphabet, under the scattered subword relation ≤, i.e., v ≤ w if and o...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2007
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2007.07.036