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

%I A213166 #12 Nov 28 2018 12:22:23
%S A213166 1,1,1,1,4,1,1,12,10,1,1,35,63,20,1,1,111,348,224,35,1,1,405,1920,
%T A213166 2027,630,56,1,1,1733,11247,17142,8600,1512,84,1,1,8666,71861,145375,
%U A213166 104175,29447,3234,120,1
%N A213166 Triangle, read by rows, of permutations of length n with k white global corners.
%C A213166 Definition of white corners (as used in the Eriksson/Linusson reference):
%C A213166 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.
%C A213166 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.
%C A213166 Equivalent definitions can use different borders and orientations.
%C A213166 Sum of entries in row n is n! (A000142).
%H A213166 K. Eriksson and S. Linusson, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v2i1r6">The size of Fulton's essential set</a>, Electronic J. Combinatorics, Vol. 2, #R6, 1995.
%e A213166 Table begins:
%e A213166 1;
%e A213166 1, 1;
%e A213166 1, 4,    1;
%e A213166 1, 12,   10,    1;
%e A213166 1, 35,   63,    20,     1;
%e A213166 1, 111,  348,   224,    35,     1;
%e A213166 1, 405,  1920,  2027,   630,    56,    1;
%e A213166 1, 1733, 11247, 17142,  8600,   1512,  84,   1;
%e A213166 1, 8666, 71861, 145375, 104175, 29447, 3234, 120, 1;
%e A213166 ...
%Y A213166 Cf. A140711 (permutations by white "local" corners).
%K A213166 nonn,tabl,more
%O A213166 1,5
%A A213166 _Olivier Gérard_, Oct 30 2012