Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001940
Mapping
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St001940: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
001 => [2,1] => [[2,2],[1]]
 => [1]
 => 1
110 => [2,1] => [[2,2],[1]]
 => [1]
 => 1
0001 => [3,1] => [[3,3],[2]]
 => [2]
 => 0
0010 => [2,1,1] => [[2,2,2],[1,1]]
 => [1,1]
 => 0
0011 => [2,2] => [[3,2],[1]]
 => [1]
 => 1
0110 => [1,2,1] => [[2,2,1],[1]]
 => [1]
 => 1
1001 => [1,2,1] => [[2,2,1],[1]]
 => [1]
 => 1
1100 => [2,2] => [[3,2],[1]]
 => [1]
 => 1
1101 => [2,1,1] => [[2,2,2],[1,1]]
 => [1,1]
 => 0
1110 => [3,1] => [[3,3],[2]]
 => [2]
 => 0
00001 => [4,1] => [[4,4],[3]]
 => [3]
 => 0
00010 => [3,1,1] => [[3,3,3],[2,2]]
 => [2,2]
 => 1
00011 => [3,2] => [[4,3],[2]]
 => [2]
 => 0
00100 => [2,1,2] => [[3,2,2],[1,1]]
 => [1,1]
 => 0
00101 => [2,1,1,1] => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => 0
00110 => [2,2,1] => [[3,3,2],[2,1]]
 => [2,1]
 => 1
00111 => [2,3] => [[4,2],[1]]
 => [1]
 => 1
01001 => [1,1,2,1] => [[2,2,1,1],[1]]
 => [1]
 => 1
01100 => [1,2,2] => [[3,2,1],[1]]
 => [1]
 => 1
01101 => [1,2,1,1] => [[2,2,2,1],[1,1]]
 => [1,1]
 => 0
01110 => [1,3,1] => [[3,3,1],[2]]
 => [2]
 => 0
10001 => [1,3,1] => [[3,3,1],[2]]
 => [2]
 => 0
10010 => [1,2,1,1] => [[2,2,2,1],[1,1]]
 => [1,1]
 => 0
10011 => [1,2,2] => [[3,2,1],[1]]
 => [1]
 => 1
10110 => [1,1,2,1] => [[2,2,1,1],[1]]
 => [1]
 => 1
11000 => [2,3] => [[4,2],[1]]
 => [1]
 => 1
11001 => [2,2,1] => [[3,3,2],[2,1]]
 => [2,1]
 => 1
11010 => [2,1,1,1] => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => 0
11011 => [2,1,2] => [[3,2,2],[1,1]]
 => [1,1]
 => 0
11100 => [3,2] => [[4,3],[2]]
 => [2]
 => 0
11101 => [3,1,1] => [[3,3,3],[2,2]]
 => [2,2]
 => 1
11110 => [4,1] => [[4,4],[3]]
 => [3]
 => 0
000001 => [5,1] => [[5,5],[4]]
 => [4]
 => 0
000010 => [4,1,1] => [[4,4,4],[3,3]]
 => [3,3]
 => 0
000011 => [4,2] => [[5,4],[3]]
 => [3]
 => 0
000100 => [3,1,2] => [[4,3,3],[2,2]]
 => [2,2]
 => 1
000101 => [3,1,1,1] => [[3,3,3,3],[2,2,2]]
 => [2,2,2]
 => 0
000110 => [3,2,1] => [[4,4,3],[3,2]]
 => [3,2]
 => 0
000111 => [3,3] => [[5,3],[2]]
 => [2]
 => 0
001000 => [2,1,3] => [[4,2,2],[1,1]]
 => [1,1]
 => 0
001001 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => [2,1,1]
 => 0
001010 => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]]
 => [1,1,1,1]
 => 0
001011 => [2,1,1,2] => [[3,2,2,2],[1,1,1]]
 => [1,1,1]
 => 0
001100 => [2,2,2] => [[4,3,2],[2,1]]
 => [2,1]
 => 1
001101 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => [2,2,1]
 => 2
001110 => [2,3,1] => [[4,4,2],[3,1]]
 => [3,1]
 => 1
001111 => [2,4] => [[5,2],[1]]
 => [1]
 => 1
010001 => [1,1,3,1] => [[3,3,1,1],[2]]
 => [2]
 => 0
010010 => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
 => [1,1]
 => 0
010011 => [1,1,2,2] => [[3,2,1,1],[1]]
 => [1]
 => 1
Description
The number of distinct parts that are equal to their multiplicity in the integer partition.