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A178249
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Table T(n,k) counts the involutions of n with longest increasing contiguous subsequence of length k.
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1
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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
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OFFSET
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1,5
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COMMENTS
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Reverse of rows converges to 1,2,8,30,118,478,2004,8666,..
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LINKS
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EXAMPLE
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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;
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MATHEMATICA
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(* 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}];
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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