A213166 Triangle, read by rows, of permutations of length n with k white global corners.

1, 1, 1, 1, 4, 1, 1, 12, 10, 1, 1, 35, 63, 20, 1, 1, 111, 348, 224, 35, 1, 1, 405, 1920, 2027, 630, 56, 1, 1, 1733, 11247, 17142, 8600, 1512, 84, 1, 1, 8666, 71861, 145375, 104175, 29447, 3234, 120, 1

Offset

1,5

Comments

Definition of white corners (as used in the Eriksson/Linusson reference):

In the representation of a permutation p as a n*n square array with n black cells at positions (i,p(i)), color in gray all cells in the row segment from each black cell to the right (east) border and in the column segment from each black cell to the bottom (south) border. Among the remaining white cells, the white corners are those without east or south white (immediate) neighbors.

In this modified sequence (not present in the Eriksson/Linusson reference), white global corners are without east or south white neighbors in the east row segment and the south column segment joining the border. This ensures that there can be at most only one white global corner for a given row or a given column. The table is triangular.

Equivalent definitions can use different borders and orientations.

Sum of entries in row n is n! (A000142).

Links

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

K. Eriksson and S. Linusson, The size of Fulton's essential set, Electronic J. Combinatorics, Vol. 2, #R6, 1995.

Example

Table begins:
1;
1, 1;
1, 4,    1;
1, 12,   10,    1;
1, 35,   63,    20,     1;
1, 111,  348,   224,    35,     1;
1, 405,  1920,  2027,   630,    56,    1;
1, 1733, 11247, 17142,  8600,   1512,  84,   1;
1, 8666, 71861, 145375, 104175, 29447, 3234, 120, 1;
...

Crossrefs

Cf. A140711 (permutations by white "local" corners).

Sequence in context: A055106 A154372 A080416 * A168619 A099759 A350819

Adjacent sequences: A213163 A213164 A213165 * A213167 A213168 A213169

Keyword

nonn,tabl,more

Author

Olivier Gérard, Oct 30 2012

Status

approved