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A307171
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Maximum number of partial loops in a diagonal Latin square of order n.
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2
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OFFSET
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1,4
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COMMENTS
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A loop in a Latin square is a sequence of cells v1=L[i1,j1] -> v2=L[i1,j2] -> v1=L[i2,j2] -> ... -> v2=L[im,j1] -> v1=L[i1,j1] of length 2*m that consists of a pair of values {v1, v2}. A partial loop is a loop of length < 2*n.
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LINKS
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EXAMPLE
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For example, the square
2 4 3 5 0 1
1 0 4 3 2 5
0 2 5 4 1 3
5 3 0 1 4 2
4 5 1 2 3 0
3 1 2 0 5 4
has a loop
2 4 . . . .
. . . . . .
. 2 . 4 . .
. . . . . .
4 . . 2 . .
. . . . . .
consisting of the sequence of cells L[1,1]=2 -> L[1,2]=4 -> L[3,2]=2 -> L[3,4]=4 -> L[5,4]=2 -> L[5,1]=4 -> L[1,1]=2 with length 6 < 12.
The total number of loops for this square is 21, all of which are partial.
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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