A346492 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.

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

Offset

1,4

Comments

First column is A002467.

Links

Table of n, a(n) for n=1..45.

FindStat, St000210: Minimum over maximum difference of elements in cycles.

Example

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

Crossrefs

Cf. A002467.

Sequence in context: A208748 A134895 A318468 * A145877 A373984 A283572

Adjacent sequences: A346489 A346490 A346491 * A346493 A346494 A346495

Keyword

nonn,tabl

Author

Peter Kagey, Jul 19 2021

Status

approved