OFFSET
0,4
COMMENTS
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(7,2) = 4, the pairs of partitions are ((4,3)/(2)), ((3,3,1)/(2), ((3,2,2)/(1,1)) and ((2,2,2,1)/(1,1));
the diagrams are:
x x 0 0 , x x 0 , x 0 0 , x 0
0 0 0 0 0 0 x 0 x 0
0 0 0 0 0
0
triangle begins:
k=0; 1 2 3 4 5 6 7
n=0; 0
n=1; 1 0
n=2; 2 0 0
n=3; 3 0 0 0
n=4; 5 1 0 0 0
n=5; 7 2 0 0 0 0
n=6; 11 5 2 0 0 0 0
n=7; 15 8 4 0 0 0 0 0
MATHEMATICA
(* see A259479 *) factor[\[Lambda]_, \[Mu]_]/; majorsweak[\[Lambda], \[Mu]]:=Block[{a1, a2, a3}, a1=Apply[Join, Table[{i, j}, {i, Length[\[Lambda]]}, {j, \[Lambda][[i]], \[Lambda][[Min[i+1, Length[\[Lambda]]]]], -1}]];
a2=Map[{First[#], First[#]>Length[\[Mu]]||\[Mu][[First[#]]]<#[[2]]}&, a1]; a3=Map[First, DeleteCases[SplitBy[a2, MatchQ[#, {_, False}]&], {{_, False}}], {2}];
Flatten[redu[Part[\[Lambda], #], Part[PadRight[\[Mu], Length[\[Lambda]], 0], #]/. 0->Sequence[]]&/@Map[Union, a3], 1]];
Table[Sum[Boole[majorsweak[\[Lambda], \[Mu]]&&redu[\[Lambda], \[Mu]]==factor[\[Lambda], \[Mu]]=={\[Lambda], \[Mu]}], {\[Lambda], Partitions[n]}, {\[Mu], Partitions[k]}], {n, 0, 12}, {k, 0, n}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Wouter Meeussen, Jul 01 2015
STATUS
approved