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 A259479 Skew diagrams, both connected or not. 10
 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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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. REFERENCES I. G. MacDonald: "Symmetric functions and Hall polynomials", Oxford University Press, 1979. Page 4. LINKS Wouter Meeussen, Table n, m, T(n,m) for n= 1..27 EXAMPLE 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)) and the diagrams are: x x 0 0 , x x 0 , x x 0 , x 0 0 , x 0 , x 0 0 0 0 0 0 0 0 x 0 x 0 x 0 0 0 0 0 0 0 triangle begins: k=0; 1 2 3 4 5 6 n=0; 1 n=1; 1 0 n=2; 2 0 0 n=3; 3 1 0 0 n=4; 5 3 0 0 0 n=5; 7 5 2 0 0 0 n=6; 11 9 6 1 0 0 0 MATHEMATICA majorsweak[left_List, right_List]:=Block[{le1=Length[left], le2=Length[right]}, If[le2>le1||Min[Sign[left-PadRight[right, le1]]]<0, False, True]]; redu1[\[Lambda]_, \[Mu]_]/; majorsweak[\[Lambda], \[Mu]]:=Delete[#, List/@DeleteCases[Table[i Boole[\[Lambda][[i]]==\[Mu][[i]]], {i, Length[\[Mu]]}], 0]]&/@{\[Lambda], \[Mu]}; redu[\[Lambda]_, \[Mu]_]/; majorsweak[\[Lambda], \[Mu]]:=TransposePartition/@Apply[redu1, TransposePartition/@redu1[\[Lambda], \[Mu]]]; Table[Sum[Boole[majorsweak[\[Lambda], \[Mu]]&&redu[\[Lambda], \[Mu]]=={\[Lambda], \[Mu]}], {\[Lambda], Partitions[n]}, {\[Mu], Partitions[k]}], {n, 0, 12}, {k, 0, n}]; CROSSREFS Cf. A259478, A259480, A259481, A161492, A227309, A006958. Sequence in context: A288437 A287736 A180969 * A238343 A238128 A238121 Adjacent sequences: A259476 A259477 A259478 * A259480 A259481 A259482 KEYWORD nonn,tabl AUTHOR Wouter Meeussen, Jun 28 2015 STATUS approved

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Last modified March 28 15:08 EDT 2023. Contains 361595 sequences. (Running on oeis4.)