cp's OEIS Frontend

A289778 Number T(n,k) of reduced decompositions for all permutations of [n] with exactly k inversions; triangle T(n,k), n>=0, 0<=k<=n*(n-1)/2, read by rows.

%I A289778 #14 Aug 19 2020 05:03:54
%S A289778 1,1,1,1,1,2,2,2,1,3,6,10,14,16,16,1,4,12,30,68,132,252,412,614,768,
%T A289778 768,1,5,20,68,210,588,1540,3778,8768,19402,40284,78276,137236,219362,
%U A289778 292864,292864,1,6,30,130,512,1864,6340,20472,62770,184748,521272,1428932
%N A289778 Number T(n,k) of reduced decompositions for all permutations of [n] with exactly k inversions; triangle T(n,k), n>=0, 0<=k<=n*(n-1)/2, read by rows.
%H A289778 Alois P. Heinz, <a href="/A289778/b289778.txt">Rows n = 0..10, flattened</a>
%H A289778 R. P. Stanley, <a href="http://dx.doi.org/10.1016/S0195-6698(84)80039-6">On the number of reduced decompositions of elements of Coxeter groups</a>, European J. Combin., 5 (1984), 359-372.
%F A289778 T(n,n*(n-1)/2) = A005118(n).
%e A289778 Triangle T(n,k) begins:
%e A289778   1;
%e A289778   1;
%e A289778   1, 1;
%e A289778   1, 2,  2,  2;
%e A289778   1, 3,  6, 10, 14,  16,  16;
%e A289778   1, 4, 12, 30, 68, 132, 252, 412, 614, 768, 768;
%e A289778   ...
%Y A289778 Row sums give A246865.
%Y A289778 Cf. A000217, A005118, A008302.
%K A289778 nonn,tabf
%O A289778 0,6
%A A289778 _Alois P. Heinz_, Jul 12 2017