Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001115
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St001115: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => [2] => [1,1,0,0]
 => [1,2] => 0
1 => [1,1] => [1,0,1,0]
 => [2,1] => 0
00 => [3] => [1,1,1,0,0,0]
 => [1,2,3] => 0
01 => [2,1] => [1,1,0,0,1,0]
 => [3,1,2] => 0
10 => [1,2] => [1,0,1,1,0,0]
 => [2,3,1] => 1
11 => [1,1,1] => [1,0,1,0,1,0]
 => [3,2,1] => 1
000 => [4] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => 0
001 => [3,1] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 0
010 => [2,2] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 1
011 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 1
100 => [1,3] => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => 0
101 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 0
110 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => 1
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => 1
0000 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => 0
0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 0
0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => 0
0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 0
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => 1
0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => 1
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => 1
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => 1
1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => [4,5,2,3,1] => 2
1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,3,1] => 2
1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => 1
1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
 => [5,3,4,2,1] => 1
1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
 => [4,5,3,2,1] => 2
1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1] => 2
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => 0
00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [6,1,2,3,4,5] => 0
00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [5,6,1,2,3,4] => 1
00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [6,5,1,2,3,4] => 1
00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [4,5,6,1,2,3] => 0
00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [6,4,5,1,2,3] => 0
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [5,6,4,1,2,3] => 1
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [6,5,4,1,2,3] => 1
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [3,4,5,6,1,2] => 1
01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [6,3,4,5,1,2] => 1
01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [5,6,3,4,1,2] => 2
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [6,5,3,4,1,2] => 2
01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [4,5,6,3,1,2] => 1
01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [6,4,5,3,1,2] => 1
01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
 => [5,6,4,3,1,2] => 2
01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [6,5,4,3,1,2] => 2
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,6,1] => 0
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [6,2,3,4,5,1] => 0
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [5,6,2,3,4,1] => 1
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [6,5,2,3,4,1] => 1
Description
The number of even descents of a permutation.