Identifier
- St000518: Binary words ⟶ ℤ
Values
=>
0=>2
1=>2
00=>3
01=>4
10=>4
11=>3
000=>4
001=>6
010=>7
011=>6
100=>6
101=>7
110=>6
111=>4
0000=>5
0001=>8
0010=>10
0011=>9
0100=>10
0101=>12
0110=>11
0111=>8
1000=>8
1001=>11
1010=>12
1011=>10
1100=>9
1101=>10
1110=>8
1111=>5
00000=>6
00001=>10
00010=>13
00011=>12
00100=>14
00101=>17
00110=>16
00111=>12
01000=>13
01001=>18
01010=>20
01011=>17
01100=>16
01101=>18
01110=>15
01111=>10
10000=>10
10001=>15
10010=>18
10011=>16
10100=>17
10101=>20
10110=>18
10111=>13
11000=>12
11001=>16
11010=>17
11011=>14
11100=>12
11101=>13
11110=>10
11111=>6
000000=>7
000001=>12
000010=>16
000011=>15
000100=>18
000101=>22
000110=>21
000111=>16
001000=>18
001001=>25
001010=>28
001011=>24
001100=>23
001101=>26
001110=>22
001111=>15
010000=>16
010001=>24
010010=>29
010011=>26
010100=>28
010101=>33
010110=>30
010111=>22
011000=>21
011001=>28
011010=>30
011011=>25
011100=>22
011101=>24
011110=>19
011111=>12
100000=>12
100001=>19
100010=>24
100011=>22
100100=>25
100101=>30
100110=>28
100111=>21
101000=>22
101001=>30
101010=>33
101011=>28
101100=>26
101101=>29
101110=>24
101111=>16
110000=>15
110001=>22
110010=>26
110011=>23
110100=>24
110101=>28
110110=>25
110111=>18
111000=>16
111001=>21
111010=>22
111011=>18
111100=>15
111101=>16
111110=>12
111111=>7
0000000=>8
0000001=>14
0000010=>19
0000011=>18
0000100=>22
0000101=>27
0000110=>26
0000111=>20
0001000=>23
0001001=>32
0001010=>36
0001011=>31
0001100=>30
0001101=>34
0001110=>29
0001111=>20
0010000=>22
0010001=>33
0010010=>40
0010011=>36
0010100=>39
0010101=>46
0010110=>42
0010111=>31
0011000=>30
0011001=>40
0011010=>43
0011011=>36
0011100=>32
0011101=>35
0011110=>28
0011111=>18
0100000=>19
0100001=>30
0100010=>38
0100011=>35
0100100=>40
0100101=>48
0100110=>45
0100111=>34
0101000=>36
0101001=>49
0101010=>54
0101011=>46
0101100=>43
0101101=>48
0101110=>40
0101111=>27
0110000=>26
0110001=>38
0110010=>45
0110011=>40
0110100=>42
0110101=>49
0110110=>44
0110111=>32
0111000=>29
0111001=>38
0111010=>40
0111011=>33
0111100=>28
0111101=>30
0111110=>23
0111111=>14
1000000=>14
1000001=>23
1000010=>30
1000011=>28
1000100=>33
1000101=>40
1000110=>38
1000111=>29
1001000=>32
1001001=>44
1001010=>49
1001011=>42
1001100=>40
1001101=>45
1001110=>38
1001111=>26
1010000=>27
1010001=>40
1010010=>48
1010011=>43
1010100=>46
1010101=>54
1010110=>49
1010111=>36
1011000=>34
1011001=>45
1011010=>48
1011011=>40
1011100=>35
1011101=>38
1011110=>30
1011111=>19
1100000=>18
1100001=>28
1100010=>35
1100011=>32
1100100=>36
1100101=>43
1100110=>40
1100111=>30
1101000=>31
1101001=>42
1101010=>46
1101011=>39
1101100=>36
1101101=>40
1101110=>33
1101111=>22
1110000=>20
1110001=>29
1110010=>34
1110011=>30
1110100=>31
1110101=>36
1110110=>32
1110111=>23
1111000=>20
1111001=>26
1111010=>27
1111011=>22
1111100=>18
1111101=>19
1111110=>14
1111111=>8
00000000=>9
00000001=>16
00000010=>22
00000011=>21
00000100=>26
00000101=>32
00000110=>31
00000111=>24
00001000=>28
00001001=>39
00001010=>44
00001011=>38
00001100=>37
00001101=>42
00001110=>36
00001111=>25
00010000=>28
00010001=>42
00010010=>51
00010011=>46
00010100=>50
00010101=>59
00010110=>54
00010111=>40
00011000=>39
00011001=>52
00011010=>56
00011011=>47
00011100=>42
00011101=>46
00011110=>37
00011111=>24
00100000=>26
00100001=>41
00100010=>52
00100011=>48
00100100=>55
00100101=>66
00100110=>62
00100111=>47
00101000=>50
00101001=>68
00101010=>75
00101011=>64
00101100=>60
00101101=>67
00101110=>56
00101111=>38
00110000=>37
00110001=>54
00110010=>64
00110011=>57
00110100=>60
00110101=>70
00110110=>63
00110111=>46
00111000=>42
00111001=>55
00111010=>58
00111011=>48
00111100=>41
00111101=>44
00111110=>34
00111111=>21
01000000=>22
01000001=>36
01000010=>47
01000011=>44
01000100=>52
01000101=>63
01000110=>60
01000111=>46
01001000=>51
01001001=>70
01001010=>78
01001011=>67
01001100=>64
01001101=>72
01001110=>61
01001111=>42
01010000=>44
01010001=>65
01010010=>78
01010011=>70
01010100=>75
01010101=>88
01010110=>80
01010111=>59
01011000=>56
01011001=>74
01011010=>79
01011011=>66
01011100=>58
01011101=>63
01011110=>50
01011111=>32
01100000=>31
01100001=>48
01100010=>60
01100011=>55
01100100=>62
01100101=>74
01100110=>69
01100111=>52
01101000=>54
01101001=>73
01101010=>80
01101011=>68
01101100=>63
01101101=>70
01101110=>58
01101111=>39
01110000=>36
01110001=>52
01110010=>61
01110011=>54
01110100=>56
01110101=>65
01110110=>58
01110111=>42
01111000=>37
01111001=>48
01111010=>50
01111011=>41
01111100=>34
01111101=>36
01111110=>27
01111111=>16
10000000=>16
10000001=>27
10000010=>36
10000011=>34
10000100=>41
10000101=>50
10000110=>48
10000111=>37
10001000=>42
10001001=>58
10001010=>65
10001011=>56
10001100=>54
10001101=>61
10001110=>52
10001111=>36
10010000=>39
10010001=>58
10010010=>70
10010011=>63
10010100=>68
10010101=>80
10010110=>73
10010111=>54
10011000=>52
10011001=>69
10011010=>74
10011011=>62
10011100=>55
10011101=>60
10011110=>48
10011111=>31
10100000=>32
10100001=>50
10100010=>63
10100011=>58
10100100=>66
10100101=>79
10100110=>74
10100111=>56
10101000=>59
10101001=>80
10101010=>88
10101011=>75
10101100=>70
10101101=>78
10101110=>65
10101111=>44
10110000=>42
10110001=>61
10110010=>72
10110011=>64
10110100=>67
10110101=>78
10110110=>70
10110111=>51
10111000=>46
10111001=>60
10111010=>63
10111011=>52
10111100=>44
10111101=>47
10111110=>36
10111111=>22
11000000=>21
11000001=>34
11000010=>44
11000011=>41
11000100=>48
11000101=>58
11000110=>55
11000111=>42
11001000=>46
11001001=>63
11001010=>70
11001011=>60
11001100=>57
11001101=>64
11001110=>54
11001111=>37
11010000=>38
11010001=>56
11010010=>67
11010011=>60
11010100=>64
11010101=>75
11010110=>68
11010111=>50
11011000=>47
11011001=>62
11011010=>66
11011011=>55
11011100=>48
11011101=>52
11011110=>41
11011111=>26
11100000=>24
11100001=>37
11100010=>46
11100011=>42
11100100=>47
11100101=>56
11100110=>52
11100111=>39
11101000=>40
11101001=>54
11101010=>59
11101011=>50
11101100=>46
11101101=>51
11101110=>42
11101111=>28
11110000=>25
11110001=>36
11110010=>42
11110011=>37
11110100=>38
11110101=>44
11110110=>39
11110111=>28
11111000=>24
11111001=>31
11111010=>32
11111011=>26
11111100=>21
11111101=>22
11111110=>16
11111111=>9
000000000=>10
000000001=>18
000000010=>25
000000011=>24
000000100=>30
000000101=>37
000000110=>36
000000111=>28
000001000=>33
000001001=>46
000001010=>52
000001011=>45
000001100=>44
000001101=>50
000001110=>43
000001111=>30
000010000=>34
000010001=>51
000010010=>62
000010011=>56
000010100=>61
000010101=>72
000010110=>66
000010111=>49
000011000=>48
000011001=>64
000011010=>69
000011011=>58
000011100=>52
000011101=>57
000011110=>46
000011111=>30
000100000=>33
000100001=>52
000100010=>66
000100011=>61
000100100=>70
000100101=>84
000100110=>79
000100111=>60
000101000=>64
000101001=>87
000101010=>96
000101011=>82
000101100=>77
000101101=>86
000101110=>72
000101111=>49
000110000=>48
000110001=>70
000110010=>83
000110011=>74
000110100=>78
000110101=>91
000110110=>82
000110111=>60
000111000=>55
000111001=>72
000111010=>76
000111011=>63
000111100=>54
000111101=>58
000111110=>45
000111111=>28
001000000=>30
001000001=>49
001000010=>64
001000011=>60
001000100=>71
001000101=>86
001000110=>82
001000111=>63
001001000=>70
001001001=>96
001001010=>107
001001011=>92
001001100=>88
001001101=>99
001001110=>84
001001111=>58
001010000=>61
001010001=>90
001010010=>108
001010011=>97
001010100=>104
001010101=>122
001010110=>111
001010111=>82
001011000=>78
001011001=>103
001011010=>110
001011011=>92
001011100=>81
001011101=>88
001011110=>70
001011111=>45
001100000=>44
001100001=>68
001100010=>85
001100011=>78
001100100=>88
001100101=>105
001100110=>98
001100111=>74
001101000=>77
001101001=>104
001101010=>114
001101011=>97
001101100=>90
001101101=>100
001101110=>83
001101111=>56
001110000=>52
001110001=>75
001110010=>88
001110011=>78
001110100=>81
001110101=>94
001110110=>84
001110111=>61
001111000=>54
001111001=>70
001111010=>73
001111011=>60
001111100=>50
001111101=>53
001111110=>40
001111111=>24
010000000=>25
010000001=>42
010000010=>56
010000011=>53
010000100=>64
010000101=>78
010000110=>75
010000111=>58
010001000=>66
010001001=>91
010001010=>102
010001011=>88
010001100=>85
010001101=>96
010001110=>82
010001111=>57
010010000=>62
010010001=>92
010010010=>111
010010011=>100
010010100=>108
010010101=>127
010010110=>116
010010111=>86
010011000=>83
010011001=>110
010011010=>118
010011011=>99
010011100=>88
010011101=>96
010011110=>77
010011111=>50
010100000=>52
010100001=>81
010100010=>102
010100011=>94
010100100=>107
010100101=>128
010100110=>120
010100111=>91
010101000=>96
010101001=>130
010101010=>143
010101011=>122
010101100=>114
010101101=>127
010101110=>106
010101111=>72
010110000=>69
010110001=>100
010110010=>118
010110011=>105
010110100=>110
010110101=>128
010110110=>115
010110111=>84
010111000=>76
010111001=>99
010111010=>104
010111011=>86
010111100=>73
010111101=>78
010111110=>60
010111111=>37
011000000=>36
011000001=>58
011000010=>75
011000011=>70
011000100=>82
011000101=>99
011000110=>94
011000111=>72
011001000=>79
011001001=>108
011001010=>120
011001011=>103
011001100=>98
011001101=>110
011001110=>93
011001111=>64
011010000=>66
011010001=>97
011010010=>116
011010011=>104
011010100=>111
011010101=>130
011010110=>118
011010111=>87
011011000=>82
011011001=>108
011011010=>115
011011011=>96
011011100=>84
011011101=>91
011011110=>72
011011111=>46
011100000=>43
011100001=>66
011100010=>82
011100011=>75
011100100=>84
011100101=>100
011100110=>93
011100111=>70
011101000=>72
011101001=>97
011101010=>106
011101011=>90
011101100=>83
011101101=>92
011101110=>76
011101111=>51
011110000=>46
011110001=>66
011110010=>77
011110011=>68
011110100=>70
011110101=>81
011110110=>72
011110111=>52
011111000=>45
011111001=>58
011111010=>60
011111011=>49
011111100=>40
011111101=>42
011111110=>31
011111111=>18
100000000=>18
100000001=>31
100000010=>42
100000011=>40
100000100=>49
100000101=>60
100000110=>58
100000111=>45
100001000=>52
100001001=>72
100001010=>81
100001011=>70
100001100=>68
100001101=>77
100001110=>66
100001111=>46
100010000=>51
100010001=>76
100010010=>92
100010011=>83
100010100=>90
100010101=>106
100010110=>97
100010111=>72
100011000=>70
100011001=>93
100011010=>100
100011011=>84
100011100=>75
100011101=>82
100011110=>66
100011111=>43
100100000=>46
100100001=>72
100100010=>91
100100011=>84
100100100=>96
100100101=>115
100100110=>108
100100111=>82
100101000=>87
100101001=>118
100101010=>130
100101011=>111
100101100=>104
100101101=>116
100101110=>97
100101111=>66
100110000=>64
100110001=>93
100110010=>110
100110011=>98
100110100=>103
100110101=>120
100110110=>108
100110111=>79
100111000=>72
100111001=>94
100111010=>99
100111011=>82
100111100=>70
100111101=>75
100111110=>58
100111111=>36
101000000=>37
101000001=>60
101000010=>78
101000011=>73
101000100=>86
101000101=>104
101000110=>99
101000111=>76
101001000=>84
101001001=>115
101001010=>128
101001011=>110
101001100=>105
101001101=>118
101001110=>100
101001111=>69
101010000=>72
101010001=>106
101010010=>127
101010011=>114
101010100=>122
101010101=>143
101010110=>130
101010111=>96
101011000=>91
101011001=>120
101011010=>128
101011011=>107
101011100=>94
101011101=>102
101011110=>81
101011111=>52
101100000=>50
101100001=>77
101100010=>96
101100011=>88
101100100=>99
101100101=>118
101100110=>110
101100111=>83
101101000=>86
101101001=>116
101101010=>127
101101011=>108
101101100=>100
101101101=>111
101101110=>92
101101111=>62
101110000=>57
101110001=>82
101110010=>96
101110011=>85
101110100=>88
101110101=>102
101110110=>91
101110111=>66
101111000=>58
101111001=>75
101111010=>78
101111011=>64
101111100=>53
101111101=>56
101111110=>42
101111111=>25
110000000=>24
110000001=>40
110000010=>53
110000011=>50
110000100=>60
110000101=>73
110000110=>70
110000111=>54
110001000=>61
110001001=>84
110001010=>94
110001011=>81
110001100=>78
110001101=>88
110001110=>75
110001111=>52
110010000=>56
110010001=>83
110010010=>100
110010011=>90
110010100=>97
110010101=>114
110010110=>104
110010111=>77
110011000=>74
110011001=>98
110011010=>105
110011011=>88
110011100=>78
110011101=>85
110011110=>68
110011111=>44
110100000=>45
110100001=>70
110100010=>88
110100011=>81
110100100=>92
110100101=>110
110100110=>103
110100111=>78
110101000=>82
110101001=>111
110101010=>122
110101011=>104
110101100=>97
110101101=>108
110101110=>90
110101111=>61
110110000=>58
110110001=>84
110110010=>99
110110011=>88
110110100=>92
110110101=>107
110110110=>96
110110111=>70
110111000=>63
110111001=>82
110111010=>86
110111011=>71
110111100=>60
110111101=>64
110111110=>49
110111111=>30
111000000=>28
111000001=>45
111000010=>58
111000011=>54
111000100=>63
111000101=>76
111000110=>72
111000111=>55
111001000=>60
111001001=>82
111001010=>91
111001011=>78
111001100=>74
111001101=>83
111001110=>70
111001111=>48
111010000=>49
111010001=>72
111010010=>86
111010011=>77
111010100=>82
111010101=>96
111010110=>87
111010111=>64
111011000=>60
111011001=>79
111011010=>84
111011011=>70
111011100=>61
111011101=>66
111011110=>52
111011111=>33
111100000=>30
111100001=>46
111100010=>57
111100011=>52
111100100=>58
111100101=>69
111100110=>64
111100111=>48
111101000=>49
111101001=>66
111101010=>72
111101011=>61
111101100=>56
111101101=>62
111101110=>51
111101111=>34
111110000=>30
111110001=>43
111110010=>50
111110011=>44
111110100=>45
111110101=>52
111110110=>46
111110111=>33
111111000=>28
111111001=>36
111111010=>37
111111011=>30
111111100=>24
111111101=>25
111111110=>18
111111111=>10
0000000001=>20
0010000001=>57
0010101101=>176
0010101011=>169
0010100111=>126
0010011101=>132
0010011011=>136
0010010111=>118
0010001111=>78
0001110101=>123
0001110011=>102
0001101101=>130
0001101011=>126
0001100111=>96
0001011101=>113
0001011011=>118
0001010111=>105
0001001111=>74
0000111101=>72
0000111011=>78
0000110111=>74
0000101111=>60
0000011111=>36
0000000000=>11
0000000110=>41
0000011000=>57
0000011110=>55
0000010010=>73
0001100000=>57
0001100110=>127
0001111000=>71
0001111110=>53
0001110010=>115
0001001000=>89
0001001110=>107
0001000010=>81
0001011010=>141
0010101010=>198
0010101000=>133
0010101100=>158
0010100100=>148
0010010100=>148
0001010100=>133
0010101110=>147
0010100000=>72
0010000100=>87
0000010100=>72
0000000010=>28
0000001110=>50
0000111110=>56
0000000100=>34
0000001010=>60
0000010110=>78
0000101110=>88
0001011110=>90
0001101110=>108
0001110110=>110
0001111010=>96
0001111100=>66
0000000101=>42
0000001101=>58
0000011101=>68
0001111101=>70
0000001001=>53
0000010101=>85
0000101101=>105
0010110001=>139
0001100001=>88
0001000001=>62
0000111111=>35
0001110100=>106
0001101100=>117
0010011100=>121
0001011100=>104
0000111100=>67
0001101010=>148
0010011010=>162
0000111010=>94
0010100110=>166
0010010110=>159
0001010110=>142
0000110110=>101
0010001110=>112
0001101001=>135
0000110001=>86
0000010001=>60
0000001100=>51
0000011001=>76
0000110011=>91
0000110100=>96
0000000011=>27
0000011011=>69
0001101111=>73
0000110101=>112
0010000010=>76
0001000011=>76
0010011110=>106
0001010000=>78
0001000100=>90
0001010101=>156
0001001011=>117
0001100011=>101
0001110111=>80
0010000000=>34
0000000111=>32
0000001111=>35
0001111111=>32
0000001011=>52
0000010111=>58
0001011111=>58
0001111001=>92
0000011010=>82
0000101010=>117
0000100101=>102
0010010001=>126
0010000101=>106
0010010101=>174
0010010011=>137
0000101011=>100
0001000111=>80
0000100111=>73
0010010010=>152
0001001010=>136
0001001001=>122
0001000101=>109
0000100011=>74
0000100100=>85
0000100010=>80
0010110000=>96
0000011100=>62
0000001000=>38
0000101100=>94
0010101111=>100
0000101000=>78
0010001000=>90
0001001100=>112
0001000110=>104
0001100100=>114
0001100010=>110
0000100110=>96
0000110010=>102
0010010000=>85
0001010010=>138
0001000000=>38
0001011001=>132
0001100101=>136
0001110001=>98
0010011001=>151
0010100101=>177
0010101001=>180
0010011111=>69
0000111001=>89
0010001101=>131
0001001101=>126
0001010001=>115
0001010011=>124
0001111011=>79
0010011000=>114
0001011000=>100
0000100000=>40
0010001011=>120
0010000111=>79
0000010011=>66
0010001100=>116
0010000110=>102
0000110000=>59
0000100001=>63
0010100011=>130
0010100001=>112
0000111000=>68
0001101000=>100
0000010000=>40
0000101001=>106
0010100010=>141
0010001001=>124
0010000011=>72
0010001010=>139
0001110000=>68
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The number of distinct subsequences in a binary word.
In contrast to the subword complexity St000294The number of distinct factors of a binary word. this is the cardinality of the set of all subsequences of not necessarily consecutive letters.
In contrast to the subword complexity St000294The number of distinct factors of a binary word. this is the cardinality of the set of all subsequences of not necessarily consecutive letters.
References
[1] Flaxman, A., Harrow, A. W., Sorkin, G. B. Strings with maximally many distinct subsequences and substrings MathSciNet:2034422
[2] Elzinga, C., Rahmann, S., Wang, H. Algorithms for subsequence combinatorics MathSciNet:2473913
[2] Elzinga, C., Rahmann, S., Wang, H. Algorithms for subsequence combinatorics MathSciNet:2473913
Code
def statistic(w): return len(Set(Subwords(w)))
Created
Jun 01, 2016 at 09:30 by Martin Rubey
Updated
Jun 01, 2016 at 09:30 by Martin Rubey
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