A178249 Table T(n,k) counts the involutions of n with longest increasing contiguous subsequence of length k.

1, 1, 1, 1, 2, 1, 1, 6, 2, 1, 1, 14, 8, 2, 1, 1, 37, 27, 8, 2, 1, 1, 96, 94, 30, 8, 2, 1, 1, 270, 338, 114, 30, 8, 2, 1, 1, 777, 1237, 446, 118, 30, 8, 2, 1, 1, 2370, 4684, 1809, 473, 118, 30, 8, 2, 1, 1, 7450, 18142, 7502, 1964, 478, 118, 30, 8, 2, 1, 1, 24485, 72524, 32093, 8414, 1998, 478, 118, 30, 8, 2, 1

Offset: 1

Author

Wouter Meeussen, Dec 20 2010

Keywords

• nonn
• tabl

Comments

Reverse of rows converges to 1,2,8,30,118,478,2004,8666,..

Examples

			T(4,2) = 6 because the 6 involutions with longest increasing contiguous subsequence lengths equal to 2 are: 1324, 1432, 2143, 3214, 3412, 4231.
Table starts:
1;
1,   1;
1,   2,   1;
1,   6,   2,   1;
1,  14,   8,   2,  1;
1,  37,  27,   8,  2, 1;
1,  96,  94,  30,  8, 2, 1;
1, 270, 338, 114, 30, 8, 2, 1;
		

Crossrefs

Cf. A008304; row sums are A000085; A047884 removes the contiguity requirement.

Programs

Mathematica

(* first do *)
Needs["Combinatorica`"]
(* then *)
maxISS[perm_List] := Max[0, (Max @@ (Length[#1]*Sign[First[#1]] & ) /@ Split[Sign[Rest[#1] - Drop[#1, -1]]] & )[perm]];classMaxISS[par_?PartitionQ]:=Count[ maxISS/@( TableauxToPermutation[FirstLexicographicTableau[par], #]&/@Tableaux[par]  ) ,#]&/@(-1+Range[ Tr[par] ]);
Table[Apply[Plus,classMaxISS/@Partitions[n]],{n,2,6}];

Extensions

Definition corrected by Wouter Meeussen, Dec 22 2010