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A351100
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Maximum number of 4-subsets of an n-set such that every 3-subset is covered at most twice.
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0
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2, 5, 9, 15, 28, 40, 60, 80, 108, 143, 182, 225, 280, 340, 405
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OFFSET
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4,1
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COMMENTS
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Maximum number of K_4^3's that can be packed in a doubled K_n^3, where K_n^m is the complete m-uniform hypergraph on n vertices.
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LINKS
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Richard K. Guy, A problem of Zarankiewicz, Research Paper No. 12, Department of Mathematics, University of Calgary, January 1967. [Annotated and scanned copy, with permission]
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FORMULA
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a(n) >= 2*A001843(n). Equality holds if n = 6k+2 or 6k+4 (Hanani).
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EXAMPLE
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a(6) = 9 because of the following optimal collection of 4-subsets:
1 2 3 4
2 3 4 5
3 4 5 6
4 5 6 1
5 6 1 2
6 1 2 3
1 2 4 5
2 3 5 6
3 4 6 1
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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