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A346492
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Triangle read by rows: T(n,k) is the number of permutations of length n such that the minimum over maximum difference of elements in cycles is exactly k; 0 <= k < n.
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0
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1, 1, 1, 4, 0, 2, 15, 2, 1, 6, 76, 8, 8, 4, 24, 455, 40, 40, 45, 20, 120, 3186, 244, 246, 254, 270, 120, 720, 25487, 1729, 1728, 1757, 1849, 1890, 840, 5040, 229384, 13948, 13960, 14096, 14540, 14792, 15120, 6720, 40320
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OFFSET
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1,4
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COMMENTS
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LINKS
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EXAMPLE
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The minimum over maximum difference of elements in cycles of the permutation (421)(53), written in cycle notation, is 2. The first cycle has maximum difference of 4-1=3, the second cycle has a maximum difference of 5-3=2, and the minimum of these is min(3,2) = 2.
The permutations whose minimum over maximum difference of elements in cycles is 0 are precisely those with a fixed point.
n\k | 0 1 2 3 4 5 6 7 8
----+--------------------------------------------------------
1 | 1
2 | 1 1
3 | 4 0 2
4 | 15 2 1 6
5 | 76 8 8 4 24
6 | 455 40 40 45 20 120
7 | 3186 244 246 254 270 120 720
8 | 25487 1729 1728 1757 1849 1890 840 5040
9 | 229384 13948 13960 14096 14540 14792 15120 6720 40320
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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