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%I #20 Aug 28 2015 13:53:46
%S 1,1,0,2,0,0,3,1,0,0,5,3,0,0,0,7,5,2,0,0,0,11,9,6,1,0,0,0,15,13,12,6,
%T 0,0,0,0,22,20,22,14,3,0,0,0,0,30,28,36,27,13,2,0,0,0,0,42,40,56,48,
%U 31,11,1,0,0,0,0,56,54,82,77,59,33,9,0,0,0,0,0,77,75,120,121,106,72,30,6,0,0,0,0,0
%N Skew diagrams, both connected or not.
%C T(n,m) counts pairs of partitions lambda of n and mu of 0<=m<=n respectively, so that the Ferrers diagram of mu does not exceed that of lambda, and that the diagrams of lambda and mu do not contain equal rows or columns.
%D I. G. MacDonald: "Symmetric functions and Hall polynomials", Oxford University Press, 1979. Page 4.
%H Wouter Meeussen, <a href="/A259479/a259479.txt">Table n, m, T(n,m) for n= 1..27</a>
%e T(6,2) = 6, the pairs of partitions are ((4,2)/(2)), ((3,3)/(2), ((3,2,1)/(2)), ((3,2,1)/(1,1)), ((2,2,2)/(1,1)) and ((2,2,1,1)/(1,1))
%e and the diagrams are:
%e x x 0 0 , x x 0 , x x 0 , x 0 0 , x 0 , x 0
%e 0 0 0 0 0 0 0 x 0 x 0 x 0
%e 0 0 0 0 0
%e 0
%e triangle begins:
%e k=0; 1 2 3 4 5 6
%e n=0; 1
%e n=1; 1 0
%e n=2; 2 0 0
%e n=3; 3 1 0 0
%e n=4; 5 3 0 0 0
%e n=5; 7 5 2 0 0 0
%e n=6; 11 9 6 1 0 0 0
%t majorsweak[left_List, right_List]:=Block[{le1=Length[left], le2=Length[right]}, If[le2>le1||Min[Sign[left-PadRight[right, le1]]]<0, False, True]];
%t redu1[\[Lambda]_,\[Mu]_]/;majorsweak[\[Lambda],\[Mu]]:=Delete[#,List/@DeleteCases[Table[i Boole[\[Lambda][[i]]==\[Mu][[i]]],{i,Length[\[Mu]]}],0]]&/@{\[Lambda],\[Mu]};
%t redu[\[Lambda]_,\[Mu]_]/;majorsweak[\[Lambda],\[Mu]]:=TransposePartition/@Apply[redu1,TransposePartition/@redu1[\[Lambda],\[Mu]]];
%t Table[Sum[Boole[majorsweak[\[Lambda],\[Mu]]&&redu[\[Lambda],\[Mu]]=={\[Lambda],\[Mu]}],{\[Lambda],Partitions[n]},{\[Mu],Partitions[k]}],{n,0,12},{k,0,n}];
%Y Cf. A259478, A259480, A259481, A161492, A227309, A006958.
%K nonn,tabl
%O 0,4
%A _Wouter Meeussen_, Jun 28 2015
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