A229729 -id:A229729 - cp's OEIS frontend

A229730 Number of separable permutations with the maximum number of occurrences of the 1-box pattern on separable permutations.

Original entry on oeis.org

0, 0, 2, 2, 8, 14, 54, 128, 466

Offset: 0

N. J. A. Sloane, Oct 01 2013

See Kitaev-Remmel for precise definition.

S. Kitaev and J. Remmel, The 1-box pattern on pattern avoiding permutations, arXiv preprint arXiv:1305.6970 [math.CO], 2013.

Cf. A229729, A363181.

A346462 Triangle read by rows: T(n,k) gives the number of permutations of length n containing exactly k instances of the 1-box pattern; 0 <= k <= n.

Original entry on oeis.org

1, 1, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 10, 4, 8, 14, 0, 40, 10, 42, 14, 90, 0, 230, 40, 226, 80, 54, 646, 0, 1580, 230, 1480, 442, 534, 128, 5242, 0, 12434, 1580, 11496, 2920, 4746, 1404, 498, 47622, 0, 110320, 12434, 101966, 22762, 45216, 13138, 7996, 1426

Offset: 0

Peter Kagey, Jul 19 2021

An instance of the 1-box pattern in a permutation pi is a letter pi_i such that pi_{i-1} or pi_{i+1} differs from pi_i by exactly 1.
Column k=0 is A002464. Columns k=2 and k=3 are given by A086852.
Main diagonal begins: 1,0,2,2,8,14,54,128,498,1426,5736,... A363181.

			The permutation 14327568 has 5 instances of the 1-box pattern:
- position 2 differs from position 3 by one,
- position 3 differs from positions 2 and 4 by one,
- position 4 differs from position 3 by one,
- position 6 differs from position 7 by one,
- position 7 differs from position 6 by one, and
positions 1, 5, and 8 differ from all of their neighbors by more than 1.
Table begins:
  n\k|  0  1    2   3    4   5   6
-----+-----------------------------
   0 |  1
   1 |  1  0
   2 |  0  0    2
   3 |  0  0    4   2
   4 |  2  0   10   4    8
   5 | 14  0   40  10   42  14
   6 | 90  0  230  40  226  80  54

Alois P. Heinz, Rows n = 0..20, flattened
FindStat, St000064: The number of one-box pattern of a permutation.
S. Kitaev, J. Remmel, The 1-box pattern on pattern avoiding permutations, arXiv:1305.6970 [math.CO], 2013.

Cf. A002464, A086852, A229729, A229730, A363181.

Row sums give A000142.

cp's OEIS Frontend

A229730 Number of separable permutations with the maximum number of occurrences of the 1-box pattern on separable permutations.

Views

Author

Keywords

Comments

Links

Crossrefs