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Identifier
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
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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.
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
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