Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000393
(load all 13 compositions to match this statistic)
Mapping
Mp00104: Binary words —reverse⟶ Binary words
St000393: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0 => 1
1 => 1 => 1
00 => 00 => 2
01 => 10 => 2
10 => 01 => 1
11 => 11 => 2
000 => 000 => 3
001 => 100 => 3
010 => 010 => 2
011 => 110 => 3
100 => 001 => 2
101 => 101 => 2
110 => 011 => 2
111 => 111 => 3
0000 => 0000 => 4
0001 => 1000 => 4
0010 => 0100 => 3
0011 => 1100 => 4
0100 => 0010 => 3
0101 => 1010 => 3
0110 => 0110 => 3
0111 => 1110 => 4
1000 => 0001 => 3
1001 => 1001 => 3
1010 => 0101 => 2
1011 => 1101 => 3
1100 => 0011 => 3
1101 => 1011 => 3
1110 => 0111 => 3
1111 => 1111 => 4
00000 => 00000 => 5
00001 => 10000 => 5
00010 => 01000 => 4
00011 => 11000 => 5
00100 => 00100 => 4
00101 => 10100 => 4
00110 => 01100 => 4
00111 => 11100 => 5
01000 => 00010 => 4
01001 => 10010 => 4
01010 => 01010 => 3
01011 => 11010 => 4
01100 => 00110 => 4
01101 => 10110 => 4
01110 => 01110 => 4
01111 => 11110 => 5
10000 => 00001 => 4
10001 => 10001 => 4
10010 => 01001 => 3
10011 => 11001 => 4
Description
The number of strictly increasing runs in a binary word.
Matching statistic: St001237
(load all 7 compositions to match this statistic)
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00331: Dyck paths —rotate triangulation counterclockwise⟶ Dyck paths
St001237: Dyck paths ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 50%
Values
0 => [2] => [1,1,0,0]
 => [1,0,1,0]
 => 3 = 1 + 2
1 => [1,1] => [1,0,1,0]
 => [1,1,0,0]
 => 3 = 1 + 2
00 => [3] => [1,1,1,0,0,0]
 => [1,0,1,1,0,0]
 => 4 = 2 + 2
01 => [2,1] => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 4 = 2 + 2
10 => [1,2] => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 3 = 1 + 2
11 => [1,1,1] => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 4 = 2 + 2
000 => [4] => [1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 5 = 3 + 2
001 => [3,1] => [1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => 5 = 3 + 2
010 => [2,2] => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 4 = 2 + 2
011 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 5 = 3 + 2
100 => [1,3] => [1,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,0,0]
 => 4 = 2 + 2
101 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => 4 = 2 + 2
110 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 4 = 2 + 2
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 5 = 3 + 2
0000 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 6 = 4 + 2
0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 6 = 4 + 2
0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5 = 3 + 2
0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 6 = 4 + 2
0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => 5 = 3 + 2
0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => 5 = 3 + 2
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 5 = 3 + 2
0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 6 = 4 + 2
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 5 = 3 + 2
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => 5 = 3 + 2
1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => 4 = 2 + 2
1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 5 = 3 + 2
1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 5 = 3 + 2
1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 5 = 3 + 2
1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 5 = 3 + 2
1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 6 = 4 + 2
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 7 = 5 + 2
00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 7 = 5 + 2
00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => 6 = 4 + 2
00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 7 = 5 + 2
00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,0,1,1,0,0]
 => 6 = 4 + 2
00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => 6 = 4 + 2
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => 6 = 4 + 2
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 7 = 5 + 2
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => 6 = 4 + 2
01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => 6 = 4 + 2
01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => 5 = 3 + 2
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0]
 => 6 = 4 + 2
01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0,1,1,0,0]
 => 6 = 4 + 2
01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => 6 = 4 + 2
01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => 6 = 4 + 2
01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 7 = 5 + 2
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 6 = 4 + 2
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => 6 = 4 + 2
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => 5 = 3 + 2
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 6 = 4 + 2
000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 6 + 2
000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 6 + 2
000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 5 + 2
000011 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 6 + 2
000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0,1,1,0,0]
 => ? = 5 + 2
000101 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,1,0,0]
 => ? = 5 + 2
000110 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0,1,0]
 => ? = 5 + 2
000111 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => ? = 6 + 2
001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,0,0,0,1,1,1,0,0,0]
 => ? = 5 + 2
001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,1,0,0,0]
 => ? = 5 + 2
001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0,1,0]
 => ? = 4 + 2
001011 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,1,0,0,0]
 => ? = 5 + 2
001100 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0,1,1,0,0]
 => ? = 5 + 2
001101 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,1,0,0]
 => ? = 5 + 2
001110 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => ? = 5 + 2
001111 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => ? = 6 + 2
010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,1,0,0,1,1,1,1,0,0,0,0]
 => ? = 5 + 2
010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,1,1,0,0,0,0]
 => ? = 5 + 2
010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0,1,0]
 => ? = 4 + 2
010011 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,0,1,1,0,0,0,0]
 => ? = 5 + 2
010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,1,0,0]
 => ? = 4 + 2
010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,1,0,0,1,0,0,1,0,0]
 => ? = 4 + 2
010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0,1,0]
 => ? = 4 + 2
010111 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,1,0,0,1,0,0,0,0]
 => ? = 5 + 2
011000 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0,1,1,1,0,0,0]
 => ? = 5 + 2
011001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,1,0,0,0]
 => ? = 5 + 2
011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
 => ? = 4 + 2
011011 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,1,0,0,0]
 => ? = 5 + 2
011100 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0,1,1,0,0]
 => ? = 5 + 2
011101 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,0,1,0,0]
 => ? = 5 + 2
011110 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => ? = 5 + 2
011111 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => ? = 6 + 2
100000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => ? = 5 + 2
100001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => ? = 5 + 2
100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0,1,0]
 => ? = 4 + 2
100011 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => ? = 5 + 2
100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,0,0,0,1,1,0,0]
 => ? = 4 + 2
100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,1,0,0,0,1,0,0]
 => ? = 4 + 2
100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
 => ? = 4 + 2
100111 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => ? = 5 + 2
101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,0,1,1,1,0,0,0]
 => ? = 4 + 2
101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,1,0,0,0]
 => ? = 4 + 2
101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0,1,0]
 => ? = 3 + 2
101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 4 + 2
101100 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0,1,1,0,0]
 => ? = 4 + 2
101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
 => ? = 4 + 2
101110 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => ? = 4 + 2
101111 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5 + 2
110000 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 5 + 2
110001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => ? = 5 + 2
Description
The number of simple modules with injective dimension at most one or dominant dimension at least one.
Matching statistic: St000245
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St000245: Permutations ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 90%
Values
0 => [2] => [1,1,0,0]
 => [2,3,1] => 1
1 => [1,1] => [1,0,1,0]
 => [3,1,2] => 1
00 => [3] => [1,1,1,0,0,0]
 => [2,3,4,1] => 2
01 => [2,1] => [1,1,0,0,1,0]
 => [2,4,1,3] => 2
10 => [1,2] => [1,0,1,1,0,0]
 => [3,1,4,2] => 1
11 => [1,1,1] => [1,0,1,0,1,0]
 => [4,1,2,3] => 2
000 => [4] => [1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => 3
001 => [3,1] => [1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => 3
010 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,4,1,5,3] => 2
011 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,5,1,3,4] => 3
100 => [1,3] => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => 2
101 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => 2
110 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => 2
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 3
0000 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,6,1] => 4
0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [2,3,4,6,1,5] => 4
0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [2,3,5,1,6,4] => 3
0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [2,3,6,1,4,5] => 4
0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,4,1,5,6,3] => 3
0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,4,1,6,3,5] => 3
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [2,5,1,3,6,4] => 3
0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [2,6,1,3,4,5] => 4
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
 => [3,1,4,5,6,2] => 3
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => 3
1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => [3,1,5,2,6,4] => 2
1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
 => [3,1,6,2,4,5] => 3
1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
 => [4,1,2,5,6,3] => 3
1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
 => [4,1,2,6,3,5] => 3
1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => 3
1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
 => [6,1,2,3,4,5] => 4
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [2,3,4,5,6,7,1] => 5
00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [2,3,4,5,7,1,6] => 5
00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [2,3,4,6,1,7,5] => 4
00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [2,3,4,7,1,5,6] => 5
00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [2,3,5,1,6,7,4] => ? = 4
00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [2,3,5,1,7,4,6] => ? = 4
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [2,3,6,1,4,7,5] => ? = 4
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [2,3,7,1,4,5,6] => ? = 5
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,4,1,5,6,7,3] => ? = 4
01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [2,4,1,5,7,3,6] => ? = 4
01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [2,4,1,6,3,7,5] => ? = 3
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [2,4,1,7,3,5,6] => ? = 4
01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [2,5,1,3,6,7,4] => ? = 4
01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [2,5,1,3,7,4,6] => ? = 4
01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
 => [2,6,1,3,4,7,5] => ? = 4
01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [2,7,1,3,4,5,6] => 5
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [3,1,4,5,6,7,2] => ? = 4
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [3,1,4,5,7,2,6] => ? = 4
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [3,1,4,6,2,7,5] => ? = 3
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [3,1,4,7,2,5,6] => ? = 4
10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [3,1,5,2,6,7,4] => ? = 3
10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [3,1,5,2,7,4,6] => ? = 3
10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [3,1,6,2,4,7,5] => ? = 3
10111 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [3,1,7,2,4,5,6] => ? = 4
11000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [4,1,2,5,6,7,3] => ? = 4
11001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [4,1,2,5,7,3,6] => ? = 4
11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [4,1,2,6,3,7,5] => ? = 3
11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [4,1,2,7,3,5,6] => ? = 4
11100 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [5,1,2,3,6,7,4] => 4
11101 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [5,1,2,3,7,4,6] => 4
11110 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [6,1,2,3,4,7,5] => 4
11111 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [7,1,2,3,4,5,6] => 5
000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [2,3,4,5,6,7,8,1] => 6
000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 6
000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [2,3,4,5,7,1,8,6] => ? = 5
000011 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [2,3,4,5,8,1,6,7] => ? = 6
000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [2,3,4,6,1,7,8,5] => ? = 5
000101 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => [2,3,4,6,1,8,5,7] => ? = 5
000110 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
 => [2,3,4,7,1,5,8,6] => ? = 5
000111 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [2,3,4,8,1,5,6,7] => ? = 6
001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => [2,3,5,1,6,7,8,4] => ? = 5
001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => [2,3,5,1,6,8,4,7] => ? = 5
001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
 => [2,3,5,1,7,4,8,6] => ? = 4
001011 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
 => [2,3,5,1,8,4,6,7] => ? = 5
001100 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
 => [2,3,6,1,4,7,8,5] => ? = 5
001101 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
 => [2,3,6,1,4,8,5,7] => ? = 5
001110 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
 => [2,3,7,1,4,5,8,6] => ? = 5
001111 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [2,3,8,1,4,5,6,7] => ? = 6
010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [2,4,1,5,6,7,8,3] => ? = 5
010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => [2,4,1,5,6,8,3,7] => ? = 5
010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
 => [2,4,1,5,7,3,8,6] => ? = 4
010011 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
 => [2,4,1,5,8,3,6,7] => ? = 5
010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
 => [2,4,1,6,3,7,8,5] => ? = 4
010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [2,4,1,6,3,8,5,7] => ? = 4
010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
 => [2,4,1,7,3,5,8,6] => ? = 4
010111 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
 => [2,4,1,8,3,5,6,7] => ? = 5
011000 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
 => [2,5,1,3,6,7,8,4] => ? = 5
011001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
 => [2,5,1,3,6,8,4,7] => ? = 5
011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
 => [2,5,1,3,7,4,8,6] => ? = 4
011011 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
 => [2,5,1,3,8,4,6,7] => ? = 5
011100 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
 => [2,6,1,3,4,7,8,5] => ? = 5
011111 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [2,8,1,3,4,5,6,7] => 6
101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [3,1,5,2,7,4,8,6] => 3
111110 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [7,1,2,3,4,5,8,6] => 5
111111 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [8,1,2,3,4,5,6,7] => 6
0000000 => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => [2,3,4,5,6,7,8,9,1] => 7
0000001 => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,7,9,1,8] => 7
0111111 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [2,9,1,3,4,5,6,7,8] => 7
1111110 => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [8,1,2,3,4,5,6,9,7] => 6
1111111 => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [9,1,2,3,4,5,6,7,8] => 7
Description
The number of ascents of a permutation.