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- W2072556229 abstract "Given any positive integern, consider partitions of the integers 1, 2, …, 2ninto two disjoint classes {ai} and {bi} withnelements in each class. Denote byMkthe number of solutions ofk=ai−bj. In the minimum overlap problem, one seeks to estimateM(n)=min maxk Mkwhere the minimum is taken over all partitions. The best known results have been 0.3564⩽lim M(n)/n⩽0.4. The author improves the upper bound to lim M(n)/n<0.3857 by using the possibility of the truth of a conjecture. This conjecture is now a theorem of Swinnerton–Dyer, which allows the further improvement to 0.3820." @default.
- W2072556229 created "2016-06-24" @default.
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- W2072556229 date "1996-05-01" @default.
- W2072556229 modified "2023-09-30" @default.
- W2072556229 title "Advances in the Minimum Overlap Problem" @default.
- W2072556229 doi "https://doi.org/10.1006/jnth.1996.0064" @default.
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