OFFSET
1,4
COMMENTS
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
Clark Kimberling and Peter J. C. Moses, Ferrers Matrices and Related Partitions of Integers
EXAMPLE
The first 4 rows of the array of SE partitions:
1
1 .. 1
2 .. 1 .. 1 .. 1 .. 1
3 .. 1 .. 2 .. 1 .. 1 .. 1 .. 1 .. 1 .. 1
Row 4, for example, represents the 4 NE partitions of 4 as follows: [3,1], [2,1,1], [1,1,1,1], listed in "Mathematica order".
MATHEMATICA
z = 10; ferrersMatrix[list_] := PadRight[Map[Table[1, {#}] &, #], {#, #} &[Max[#, Length[#]]]] &[list]; cornerPart[list_] := Module[{f = ferrersMatrix[list], u, l, ur, lr, nw, ne, se, sw}, {u, l} = {UpperTriangularize[#, 1], LowerTriangularize[#]} &[f]; {ur, lr} = {UpperTriangularize[#, 1], LowerTriangularize[#]} &[Reverse[f]]; {nw, ne, se, sw} = {Total[Transpose[u]] + Total[l], Total[ur] + Total[Transpose[lr]], Total[u] + Total[Transpose[l]], Total[Transpose[ur]] + Total[lr]}; Map[DeleteCases[Reverse[Sort[#]], 0] &, {nw, ne, se, sw}]]; cornerParts[n_] := Map[#[[Reverse[Ordering[PadRight[#]]]]] &, Map[DeleteDuplicates[#] &, Transpose[Map[cornerPart, IntegerPartitions[n]]]]]; cP = Map[cornerParts, Range[z]];
Flatten[Map[cP[[#, 1]] &, Range[Length[cP]]]](*NW corner: A237981*)
Flatten[Map[cP[[#, 2]] &, Range[Length[cP]]]](*NE corner: A237982*)
Flatten[Map[cP[[#, 3]] &, Range[Length[cP]]]](*SE corner: A237983*)
Flatten[Map[cP[[#, 4]] &, Range[Length[cP]]]](*SW corner: A237982*)
(* Peter J. C. Moses, Feb 25 2014 *)
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Clark Kimberling and Peter J. C. Moses, Feb 25 2014
STATUS
approved