Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000816
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
St000816: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => [2] => 1
1 => [1,1] => 1
00 => [3] => 1
01 => [2,1] => 1
10 => [1,2] => 1
11 => [1,1,1] => 1
000 => [4] => 1
001 => [3,1] => 1
010 => [2,2] => 2
011 => [2,1,1] => 1
100 => [1,3] => 2
101 => [1,2,1] => 1
110 => [1,1,2] => 1
111 => [1,1,1,1] => 1
0000 => [5] => 1
0001 => [4,1] => 1
0010 => [3,2] => 3
0011 => [3,1,1] => 1
0100 => [2,3] => 2
0101 => [2,2,1] => 2
0110 => [2,1,2] => 1
0111 => [2,1,1,1] => 1
1000 => [1,4] => 3
1001 => [1,3,1] => 2
1010 => [1,2,2] => 2
1011 => [1,2,1,1] => 1
1100 => [1,1,3] => 3
1101 => [1,1,2,1] => 1
1110 => [1,1,1,2] => 1
1111 => [1,1,1,1,1] => 1
00000 => [6] => 1
00001 => [5,1] => 1
00010 => [4,2] => 4
00011 => [4,1,1] => 1
00100 => [3,3] => 5
00101 => [3,2,1] => 3
00110 => [3,1,2] => 1
00111 => [3,1,1,1] => 1
01000 => [2,4] => 5
01001 => [2,3,1] => 2
01010 => [2,2,2] => 5
01011 => [2,2,1,1] => 2
01100 => [2,1,3] => 3
01101 => [2,1,2,1] => 1
01110 => [2,1,1,2] => 1
01111 => [2,1,1,1,1] => 1
10000 => [1,5] => 4
10001 => [1,4,1] => 3
10010 => [1,3,2] => 5
10011 => [1,3,1,1] => 2
Description
The number of standard composition tableaux of the composition. See [1, Def. 4.2.6]. Apparently, the total number of tableaux of given size is the number of involutions.