Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001153
Mapping
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
St001153: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => [1] => [1,0]
 => {{1}}
 => 0
1 => [1] => [1,0]
 => {{1}}
 => 0
00 => [2] => [1,1,0,0]
 => {{1,2}}
 => 0
01 => [1,1] => [1,0,1,0]
 => {{1},{2}}
 => 1
10 => [1,1] => [1,0,1,0]
 => {{1},{2}}
 => 1
11 => [2] => [1,1,0,0]
 => {{1,2}}
 => 0
000 => [3] => [1,1,1,0,0,0]
 => {{1,2,3}}
 => 0
001 => [2,1] => [1,1,0,0,1,0]
 => {{1,2},{3}}
 => 0
010 => [1,1,1] => [1,0,1,0,1,0]
 => {{1},{2},{3}}
 => 1
011 => [1,2] => [1,0,1,1,0,0]
 => {{1},{2,3}}
 => 1
100 => [1,2] => [1,0,1,1,0,0]
 => {{1},{2,3}}
 => 1
101 => [1,1,1] => [1,0,1,0,1,0]
 => {{1},{2},{3}}
 => 1
110 => [2,1] => [1,1,0,0,1,0]
 => {{1,2},{3}}
 => 0
111 => [3] => [1,1,1,0,0,0]
 => {{1,2,3}}
 => 0
0000 => [4] => [1,1,1,1,0,0,0,0]
 => {{1,2,3,4}}
 => 0
0001 => [3,1] => [1,1,1,0,0,0,1,0]
 => {{1,2,3},{4}}
 => 1
0010 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => {{1,2},{3},{4}}
 => 1
0011 => [2,2] => [1,1,0,0,1,1,0,0]
 => {{1,2},{3,4}}
 => 0
0100 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => {{1},{2},{3,4}}
 => 1
0101 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => {{1},{2},{3},{4}}
 => 2
0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => {{1},{2,3},{4}}
 => 2
0111 => [1,3] => [1,0,1,1,1,0,0,0]
 => {{1},{2,3,4}}
 => 1
1000 => [1,3] => [1,0,1,1,1,0,0,0]
 => {{1},{2,3,4}}
 => 1
1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => {{1},{2,3},{4}}
 => 2
1010 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => {{1},{2},{3},{4}}
 => 2
1011 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => {{1},{2},{3,4}}
 => 1
1100 => [2,2] => [1,1,0,0,1,1,0,0]
 => {{1,2},{3,4}}
 => 0
1101 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => {{1,2},{3},{4}}
 => 1
1110 => [3,1] => [1,1,1,0,0,0,1,0]
 => {{1,2,3},{4}}
 => 1
1111 => [4] => [1,1,1,1,0,0,0,0]
 => {{1,2,3,4}}
 => 0
00000 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => {{1,2,3,4,5}}
 => 0
00001 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => {{1,2,3,4},{5}}
 => 0
00010 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => {{1,2,3},{4},{5}}
 => 1
00011 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => {{1,2,3},{4,5}}
 => 1
00100 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => {{1,2},{3},{4,5}}
 => 1
00101 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => {{1,2},{3},{4},{5}}
 => 1
00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => {{1,2},{3,4},{5}}
 => 0
00111 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => {{1,2},{3,4,5}}
 => 0
01000 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
 => {{1},{2},{3,4,5}}
 => 1
01001 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
 => {{1},{2},{3,4},{5}}
 => 1
01010 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
 => {{1},{2},{3},{4},{5}}
 => 2
01011 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
 => {{1},{2},{3},{4,5}}
 => 2
01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => {{1},{2,3},{4,5}}
 => 2
01101 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
 => {{1},{2,3},{4},{5}}
 => 2
01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => {{1},{2,3,4},{5}}
 => 1
01111 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
 => {{1},{2,3,4,5}}
 => 1
10000 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
 => {{1},{2,3,4,5}}
 => 1
10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => {{1},{2,3,4},{5}}
 => 1
10010 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
 => {{1},{2,3},{4},{5}}
 => 2
10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => {{1},{2,3},{4,5}}
 => 2
Description
The number of blocks with even minimum in a set partition.