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Search: id:A107431
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| A107431 |
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Triangle read by rows: T(n,k) = maximal number of rounds for the social golfer problem with n groups of k golfers (n >= 2, 2 <= k <= n). |
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+0
2
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| 3, 5, 4, 7, 4, 5, 9, 7, 5, 6, 11, 8, 7, 6, 3, 13, 10, 9
(list; table; graph; listen)
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OFFSET
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2,1
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COMMENT
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The problem is to find the largest number of rounds of golf that can be arranged with n*k golfers who play in n groups of k. No golfer may play in the same group as any other golfer twice (i.e. maximum socialisation is achieved).
T(6,6) cannot be 4 since this would be equivalent to a pair of mutually orthogonal Latin squares of order 6.
T(n,k) = 1 for values of n and k outside this range.
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LINKS
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W. Harvey, Social Golfer
W. Harvey, Summary Table
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EXAMPLE
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Triangle begins:
3
5 4
7 4 5
9 7 5 6
11 8 7 6 3
T(2,2) = 3 from { 12/34, 13/24, 14/23 }.
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CROSSREFS
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Column 3 gives A107432.
Sequence in context: A064425 A094761 A114748 this_sequence A023859 A096457 A082568
Adjacent sequences: A107428 A107429 A107430 this_sequence A107432 A107433 A107434
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KEYWORD
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nonn,tabl
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), following a tip from Ed Pegg Jr., May 28 2005
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EXTENSIONS
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The next term T(7,5) is known to be either 7 or 8.
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