Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001114
Mapping
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
St001114: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
00 => [2] => [1,1,0,0]
 => [2,1] => 1
01 => [1,1] => [1,0,1,0]
 => [1,2] => 0
10 => [1,1] => [1,0,1,0]
 => [1,2] => 0
11 => [2] => [1,1,0,0]
 => [2,1] => 1
000 => [3] => [1,1,1,0,0,0]
 => [3,2,1] => 1
001 => [2,1] => [1,1,0,0,1,0]
 => [2,1,3] => 1
010 => [1,1,1] => [1,0,1,0,1,0]
 => [1,2,3] => 0
011 => [1,2] => [1,0,1,1,0,0]
 => [1,3,2] => 0
100 => [1,2] => [1,0,1,1,0,0]
 => [1,3,2] => 0
101 => [1,1,1] => [1,0,1,0,1,0]
 => [1,2,3] => 0
110 => [2,1] => [1,1,0,0,1,0]
 => [2,1,3] => 1
111 => [3] => [1,1,1,0,0,0]
 => [3,2,1] => 1
0000 => [4] => [1,1,1,1,0,0,0,0]
 => [4,3,2,1] => 2
0001 => [3,1] => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 1
0010 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 1
0011 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 2
0100 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 1
0101 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,2,3,4] => 0
0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 0
0111 => [1,3] => [1,0,1,1,1,0,0,0]
 => [1,4,3,2] => 1
1000 => [1,3] => [1,0,1,1,1,0,0,0]
 => [1,4,3,2] => 1
1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 0
1010 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,2,3,4] => 0
1011 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 1
1100 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 2
1101 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 1
1110 => [3,1] => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 1
1111 => [4] => [1,1,1,1,0,0,0,0]
 => [4,3,2,1] => 2
00000 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => [5,4,3,2,1] => 2
00001 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 2
00010 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
00011 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
00100 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => 1
00101 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => 1
00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 2
00111 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 2
01000 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,4,3] => 1
01001 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => 1
01010 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5] => 0
01011 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,4] => 0
01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => 0
01101 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => 0
01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => [1,4,3,2,5] => 1
01111 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => 1
10000 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => 1
10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => [1,4,3,2,5] => 1
10010 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => 0
10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => 0
10100 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,4] => 0
10101 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5] => 0
Description
The number of odd descents of a permutation.