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Identifier
Values
=>
0=>0 1=>0 00=>0 01=>1 10=>0 11=>0 000=>0 001=>3 010=>1 011=>3 100=>0 101=>1 110=>0 111=>0 0000=>0 0001=>6 0010=>3 0011=>8 0100=>1 0101=>5 0110=>3 0111=>6 1000=>0 1001=>3 1010=>1 1011=>3 1100=>0 1101=>1 1110=>0 1111=>0 00000=>0 00001=>10 00010=>6 00011=>15 00100=>3 00101=>11 00110=>8 00111=>15 01000=>1 01001=>8 01010=>5 01011=>11 01100=>3 01101=>8 01110=>6 01111=>10 10000=>0 10001=>6 10010=>3 10011=>8 10100=>1 10101=>5 10110=>3 10111=>6 11000=>0 11001=>3 11010=>1 11011=>3 11100=>0 11101=>1 11110=>0 11111=>0 000000=>0 000001=>15 000010=>10 000011=>24 000100=>6 000101=>19 000110=>15 000111=>27 001000=>3 001001=>15 001010=>11 001011=>22 001100=>8 001101=>18 001110=>15 001111=>24 010000=>1 010001=>12 010010=>8 010011=>18 010100=>5 010101=>14 010110=>11 010111=>19 011000=>3 011001=>11 011010=>8 011011=>15 011100=>6 011101=>12 011110=>10 011111=>15 100000=>0 100001=>10 100010=>6 100011=>15 100100=>3 100101=>11 100110=>8 100111=>15 101000=>1 101001=>8 101010=>5 101011=>11 101100=>3 101101=>8 101110=>6 101111=>10 110000=>0 110001=>6 110010=>3 110011=>8 110100=>1 110101=>5 110110=>3 110111=>6 111000=>0 111001=>3 111010=>1 111011=>3 111100=>0 111101=>1 111110=>0 111111=>0 0000000=>0 0000001=>21 0000010=>15 0000011=>35 0000100=>10 0000101=>29 0000110=>24 0000111=>42 0001000=>6 0001001=>24 0001010=>19 0001011=>36 0001100=>15 0001101=>31 0001110=>27 0001111=>42 0010000=>3 0010001=>20 0010010=>15 0010011=>31 0010100=>11 0010101=>26 0010110=>22 0010111=>36 0011000=>8 0011001=>22 0011010=>18 0011011=>31 0011100=>15 0011101=>27 0011110=>24 0011111=>35 0100000=>1 0100001=>17 0100010=>12 0100011=>27 0100100=>8 0100101=>22 0100110=>18 0100111=>31 0101000=>5 0101001=>18 0101010=>14 0101011=>26 0101100=>11 0101101=>22 0101110=>19 0101111=>29 0110000=>3 0110001=>15 0110010=>11 0110011=>22 0110100=>8 0110101=>18 0110110=>15 0110111=>24 0111000=>6 0111001=>15 0111010=>12 0111011=>20 0111100=>10 0111101=>17 0111110=>15 0111111=>21 1000000=>0 1000001=>15 1000010=>10 1000011=>24 1000100=>6 1000101=>19 1000110=>15 1000111=>27 1001000=>3 1001001=>15 1001010=>11 1001011=>22 1001100=>8 1001101=>18 1001110=>15 1001111=>24 1010000=>1 1010001=>12 1010010=>8 1010011=>18 1010100=>5 1010101=>14 1010110=>11 1010111=>19 1011000=>3 1011001=>11 1011010=>8 1011011=>15 1011100=>6 1011101=>12 1011110=>10 1011111=>15 1100000=>0 1100001=>10 1100010=>6 1100011=>15 1100100=>3 1100101=>11 1100110=>8 1100111=>15 1101000=>1 1101001=>8 1101010=>5 1101011=>11 1101100=>3 1101101=>8 1101110=>6 1101111=>10 1110000=>0 1110001=>6 1110010=>3 1110011=>8 1110100=>1 1110101=>5 1110110=>3 1110111=>6 1111000=>0 1111001=>3 1111010=>1 1111011=>3 1111100=>0 1111101=>1 1111110=>0 1111111=>0 00000000=>0 00000001=>28 00000010=>21 00000011=>48 00000100=>15 00000101=>41 00000110=>35 00000111=>60 00001000=>10 00001001=>35 00001010=>29 00001011=>53 00001100=>24 00001101=>47 00001110=>42 00001111=>64 00010000=>6 00010001=>30 00010010=>24 00010011=>47 00010100=>19 00010101=>41 00010110=>36 00010111=>57 00011000=>15 00011001=>36 00011010=>31 00011011=>51 00011100=>27 00011101=>46 00011110=>42 00011111=>60 00100000=>3 00100001=>26 00100010=>20 00100011=>42 00100100=>15 00100101=>36 00100110=>31 00100111=>51 00101000=>11 00101001=>31 00101010=>26 00101011=>45 00101100=>22 00101101=>40 00101110=>36 00101111=>53 00110000=>8 00110001=>27 00110010=>22 00110011=>40 00110100=>18 00110101=>35 00110110=>31 00110111=>47 00111000=>15 00111001=>31 00111010=>27 00111011=>42 00111100=>24 00111101=>38 00111110=>35 00111111=>48 01000000=>1 01000001=>23 01000010=>17 01000011=>38 01000100=>12 01000101=>32 01000110=>27 01000111=>46 01001000=>8 01001001=>27 01001010=>22 01001011=>40 01001100=>18 01001101=>35 01001110=>31 01001111=>47 01010000=>5 01010001=>23 01010010=>18 01010011=>35 01010100=>14 01010101=>30 01010110=>26 01010111=>41 01011000=>11 01011001=>26 01011010=>22 01011011=>36 01011100=>19 01011101=>32 01011110=>29 01011111=>41 01100000=>3 01100001=>20 01100010=>15 01100011=>31 01100100=>11 01100101=>26 01100110=>22 01100111=>36 01101000=>8 01101001=>22 01101010=>18 01101011=>31 01101100=>15 01101101=>27 01101110=>24 01101111=>35 01110000=>6 01110001=>19 01110010=>15 01110011=>27 01110100=>12 01110101=>23 01110110=>20 01110111=>30 01111000=>10 01111001=>20 01111010=>17 01111011=>26 01111100=>15 01111101=>23 01111110=>21 01111111=>28 10000000=>0 10000001=>21 10000010=>15 10000011=>35 10000100=>10 10000101=>29 10000110=>24 10000111=>42 10001000=>6 10001001=>24 10001010=>19 10001011=>36 10001100=>15 10001101=>31 10001110=>27 10001111=>42 10010000=>3 10010001=>20 10010010=>15 10010011=>31 10010100=>11 10010101=>26 10010110=>22 10010111=>36 10011000=>8 10011001=>22 10011010=>18 10011011=>31 10011100=>15 10011101=>27 10011110=>24 10011111=>35 10100000=>1 10100001=>17 10100010=>12 10100011=>27 10100100=>8 10100101=>22 10100110=>18 10100111=>31 10101000=>5 10101001=>18 10101010=>14 10101011=>26 10101100=>11 10101101=>22 10101110=>19 10101111=>29 10110000=>3 10110001=>15 10110010=>11 10110011=>22 10110100=>8 10110101=>18 10110110=>15 10110111=>24 10111000=>6 10111001=>15 10111010=>12 10111011=>20 10111100=>10 10111101=>17 10111110=>15 10111111=>21 11000000=>0 11000001=>15 11000010=>10 11000011=>24 11000100=>6 11000101=>19 11000110=>15 11000111=>27 11001000=>3 11001001=>15 11001010=>11 11001011=>22 11001100=>8 11001101=>18 11001110=>15 11001111=>24 11010000=>1 11010001=>12 11010010=>8 11010011=>18 11010100=>5 11010101=>14 11010110=>11 11010111=>19 11011000=>3 11011001=>11 11011010=>8 11011011=>15 11011100=>6 11011101=>12 11011110=>10 11011111=>15 11100000=>0 11100001=>10 11100010=>6 11100011=>15 11100100=>3 11100101=>11 11100110=>8 11100111=>15 11101000=>1 11101001=>8 11101010=>5 11101011=>11 11101100=>3 11101101=>8 11101110=>6 11101111=>10 11110000=>0 11110001=>6 11110010=>3 11110011=>8 11110100=>1 11110101=>5 11110110=>3 11110111=>6 11111000=>0 11111001=>3 11111010=>1 11111011=>3 11111100=>0 11111101=>1 11111110=>0 11111111=>0 000000000=>0 000000001=>36 000000010=>28 000000011=>63 000000100=>21 000000101=>55 000000110=>48 000000111=>81 000001000=>15 000001001=>48 000001010=>41 000001011=>73 000001100=>35 000001101=>66 000001110=>60 000001111=>90 000010000=>10 000010001=>42 000010010=>35 000010011=>66 000010100=>29 000010101=>59 000010110=>53 000010111=>82 000011000=>24 000011001=>53 000011010=>47 000011011=>75 000011100=>42 000011101=>69 000011110=>64 000011111=>90 000100000=>6 000100001=>37 000100010=>30 000100011=>60 000100100=>24 000100101=>53 000100110=>47 000100111=>75 000101000=>19 000101001=>47 000101010=>41 000101011=>68 000101100=>36 000101101=>62 000101110=>57 000101111=>82 000110000=>15 000110001=>42 000110010=>36 000110011=>62 000110100=>31 000110101=>56 000110110=>51 000110111=>75 000111000=>27 000111001=>51 000111010=>46 000111011=>69 000111100=>42 000111101=>64 000111110=>60 000111111=>81 001000000=>3 001000001=>33 001000010=>26 001000011=>55 001000100=>20 001000101=>48 001000110=>42 001000111=>69 001001000=>15 001001001=>42 001001010=>36 001001011=>62 001001100=>31 001001101=>56 001001110=>51 001001111=>75 001010000=>11 001010001=>37 001010010=>31 001010011=>56 001010100=>26 001010101=>50 001010110=>45 001010111=>68 001011000=>22 001011001=>45 001011010=>40 001011011=>62 001011100=>36 001011101=>57 001011110=>53 001011111=>73 001100000=>8 001100001=>33 001100010=>27 001100011=>51 001100100=>22 001100101=>45 001100110=>40 001100111=>62 001101000=>18 001101001=>40 001101010=>35 001101011=>56 001101100=>31 001101101=>51 001101110=>47 001101111=>66 001110000=>15 001110001=>36 001110010=>31 001110011=>51 001110100=>27 001110101=>46 001110110=>42 001110111=>60 001111000=>24 001111001=>42 001111010=>38 001111011=>55 001111100=>35 001111101=>51 001111110=>48 001111111=>63 010000000=>1 010000001=>30 010000010=>23 010000011=>51 010000100=>17 010000101=>44 010000110=>38 010000111=>64 010001000=>12 010001001=>38 010001010=>32 010001011=>57 010001100=>27 010001101=>51 010001110=>46 010001111=>69 010010000=>8 010010001=>33 010010010=>27 010010011=>51 010010100=>22 010010101=>45 010010110=>40 010010111=>62 010011000=>18 010011001=>40 010011010=>35 010011011=>56 010011100=>31 010011101=>51 010011110=>47 010011111=>66 010100000=>5 010100001=>29 010100010=>23 010100011=>46 010100100=>18 010100101=>40 010100110=>35 010100111=>56 010101000=>14 010101001=>35 010101010=>30 010101011=>50 010101100=>26 010101101=>45 010101110=>41 010101111=>59 010110000=>11 010110001=>31 010110010=>26 010110011=>45 010110100=>22 010110101=>40 010110110=>36 010110111=>53 010111000=>19 010111001=>36 010111010=>32 010111011=>48 010111100=>29 010111101=>44 010111110=>41 010111111=>55 011000000=>3 011000001=>26 011000010=>20 011000011=>42 011000100=>15 011000101=>36 011000110=>31 011000111=>51 011001000=>11 011001001=>31 011001010=>26 011001011=>45 011001100=>22 011001101=>40 011001110=>36 011001111=>53 011010000=>8 011010001=>27 011010010=>22 011010011=>40 011010100=>18 011010101=>35 011010110=>31 011010111=>47 011011000=>15 011011001=>31 011011010=>27 011011011=>42 011011100=>24 011011101=>38 011011110=>35 011011111=>48 011100000=>6 011100001=>24 011100010=>19 011100011=>36 011100100=>15 011100101=>31 011100110=>27 011100111=>42 011101000=>12 011101001=>27 011101010=>23 011101011=>37 011101100=>20 011101101=>33 011101110=>30 011101111=>42 011110000=>10 011110001=>24 011110010=>20 011110011=>33 011110100=>17 011110101=>29 011110110=>26 011110111=>37 011111000=>15 011111001=>26 011111010=>23 011111011=>33 011111100=>21 011111101=>30 011111110=>28 011111111=>36 100000000=>0 100000001=>28 100000010=>21 100000011=>48 100000100=>15 100000101=>41 100000110=>35 100000111=>60 100001000=>10 100001001=>35 100001010=>29 100001011=>53 100001100=>24 100001101=>47 100001110=>42 100001111=>64 100010000=>6 100010001=>30 100010010=>24 100010011=>47 100010100=>19 100010101=>41 100010110=>36 100010111=>57 100011000=>15 100011001=>36 100011010=>31 100011011=>51 100011100=>27 100011101=>46 100011110=>42 100011111=>60 100100000=>3 100100001=>26 100100010=>20 100100011=>42 100100100=>15 100100101=>36 100100110=>31 100100111=>51 100101000=>11 100101001=>31 100101010=>26 100101011=>45 100101100=>22 100101101=>40 100101110=>36 100101111=>53 100110000=>8 100110001=>27 100110010=>22 100110011=>40 100110100=>18 100110101=>35 100110110=>31 100110111=>47 100111000=>15 100111001=>31 100111010=>27 100111011=>42 100111100=>24 100111101=>38 100111110=>35 100111111=>48 101000000=>1 101000001=>23 101000010=>17 101000011=>38 101000100=>12 101000101=>32 101000110=>27 101000111=>46 101001000=>8 101001001=>27 101001010=>22 101001011=>40 101001100=>18 101001101=>35 101001110=>31 101001111=>47 101010000=>5 101010001=>23 101010010=>18 101010011=>35 101010100=>14 101010101=>30 101010110=>26 101010111=>41 101011000=>11 101011001=>26 101011010=>22 101011011=>36 101011100=>19 101011101=>32 101011110=>29 101011111=>41 101100000=>3 101100001=>20 101100010=>15 101100011=>31 101100100=>11 101100101=>26 101100110=>22 101100111=>36 101101000=>8 101101001=>22 101101010=>18 101101011=>31 101101100=>15 101101101=>27 101101110=>24 101101111=>35 101110000=>6 101110001=>19 101110010=>15 101110011=>27 101110100=>12 101110101=>23 101110110=>20 101110111=>30 101111000=>10 101111001=>20 101111010=>17 101111011=>26 101111100=>15 101111101=>23 101111110=>21 101111111=>28 110000000=>0 110000001=>21 110000010=>15 110000011=>35 110000100=>10 110000101=>29 110000110=>24 110000111=>42 110001000=>6 110001001=>24 110001010=>19 110001011=>36 110001100=>15 110001101=>31 110001110=>27 110001111=>42 110010000=>3 110010001=>20 110010010=>15 110010011=>31 110010100=>11 110010101=>26 110010110=>22 110010111=>36 110011000=>8 110011001=>22 110011010=>18 110011011=>31 110011100=>15 110011101=>27 110011110=>24 110011111=>35 110100000=>1 110100001=>17 110100010=>12 110100011=>27 110100100=>8 110100101=>22 110100110=>18 110100111=>31 110101000=>5 110101001=>18 110101010=>14 110101011=>26 110101100=>11 110101101=>22 110101110=>19 110101111=>29 110110000=>3 110110001=>15 110110010=>11 110110011=>22 110110100=>8 110110101=>18 110110110=>15 110110111=>24 110111000=>6 110111001=>15 110111010=>12 110111011=>20 110111100=>10 110111101=>17 110111110=>15 110111111=>21 111000000=>0 111000001=>15 111000010=>10 111000011=>24 111000100=>6 111000101=>19 111000110=>15 111000111=>27 111001000=>3 111001001=>15 111001010=>11 111001011=>22 111001100=>8 111001101=>18 111001110=>15 111001111=>24 111010000=>1 111010001=>12 111010010=>8 111010011=>18 111010100=>5 111010101=>14 111010110=>11 111010111=>19 111011000=>3 111011001=>11 111011010=>8 111011011=>15 111011100=>6 111011101=>12 111011110=>10 111011111=>15 111100000=>0 111100001=>10 111100010=>6 111100011=>15 111100100=>3 111100101=>11 111100110=>8 111100111=>15 111101000=>1 111101001=>8 111101010=>5 111101011=>11 111101100=>3 111101101=>8 111101110=>6 111101111=>10 111110000=>0 111110001=>6 111110010=>3 111110011=>8 111110100=>1 111110101=>5 111110110=>3 111110111=>6 111111000=>0 111111001=>3 111111010=>1 111111011=>3 111111100=>0 111111101=>1 111111110=>0 111111111=>0 0000000001=>45 0010000001=>41 0010101101=>73 0010101011=>79 0010100111=>86 0010011101=>80 0010011011=>86 0010010111=>93 0010001111=>101 0001110101=>74 0001110011=>80 0001101101=>80 0001101011=>86 0001100111=>93 0001011101=>87 0001011011=>93 0001010111=>100 0001001111=>108 0000111101=>95 0000111011=>101 0000110111=>108 0000101111=>116 0000011111=>125 0000000000=>0 0000000110=>63 0000011000=>35 0000011110=>90 0000010010=>48 0001100000=>15 0001100110=>62 0001111000=>42 0001111110=>81 0001110010=>51 0001001000=>24 0001001110=>75 0001000010=>37 0001011010=>62 0010101010=>50 0010101000=>26 0010101100=>45 0010100100=>31 0010010100=>36 0001010100=>41 0010101110=>68 0010100000=>11 0010000100=>26 0000010100=>41 0000000010=>36 0000001110=>81 0000111110=>90 0000000100=>28 0000001010=>55 0000010110=>73 0000101110=>82 0001011110=>82 0001101110=>75 0001110110=>69 0001111010=>64 0001111100=>60 0000000101=>71 0000001101=>88 0000011101=>96 0001111101=>85 0000001001=>63 0000010101=>80 0000101101=>88 0010110001=>51 0001100001=>49 0001000001=>45 0000111111=>120 0001110100=>46 0001101100=>51 0010011100=>51 0001011100=>57 0000111100=>64 0001101010=>56 0010011010=>56 0000111010=>69 0010100110=>56 0010010110=>62 0001010110=>68 0000110110=>75 0010001110=>69 0001101001=>62 0000110001=>60 0000010001=>56 0000001100=>48 0000011001=>73 0000110011=>88 0000110100=>47 0000000011=>80 0000011011=>103 0001101111=>103 0000110101=>81 0010000010=>33 0001000011=>75 0010011110=>75 0001010000=>19 0001000100=>30 0001010101=>74 0001001011=>88 0001100011=>75 0001110111=>96 0010000000=>3 0000000111=>105 0000001111=>120 0001111111=>105 0000001011=>96 0000010111=>111 0001011111=>111 0001111001=>69 0000011010=>66 0000101010=>59 0000100101=>73 0010010001=>49 0010000101=>62 0010010101=>68 0010010011=>75 0000101011=>95 0001000111=>96 0000100111=>103 0010010010=>42 0001001010=>53 0001001001=>60 0001000101=>67 0000100011=>81 0000100100=>35 0000100010=>42 0010110000=>22 0000011100=>60 0000001000=>21 0000101100=>53 0010101111=>95 0000101000=>29 0010001000=>20 0001001100=>47 0001000110=>60 0001100100=>36 0001100010=>42 0000100110=>66 0000110010=>53 0010010000=>15 0001010010=>47 0001000000=>6 0001011001=>68 0001100101=>68 0001110001=>57 0010011001=>62 0010100101=>62 0010101001=>56 0010011111=>103 0000111001=>75 0010001101=>75 0001001101=>81 0001010001=>54 0001010011=>81 0001111011=>90 0010011000=>31 0001011000=>36 0000100000=>10 0010001011=>82 0010000111=>90 0000010011=>88 0010001100=>42 0010000110=>55 0000110000=>24 0000100001=>50 0010100011=>69 0010100001=>44 0000111000=>42 0001101000=>31 0000010000=>15 0000101001=>66 0010100010=>37 0010001001=>55 0010000011=>70 0010001010=>48 0001110000=>27
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Description
The non-inversion sum of a binary word.
A pair $a < b$ is an noninversion of a binary word $w = w_1 \cdots w_n$ if $w_a < w_b$. The non-inversion sum is given by $\sum(b-a)$ over all non-inversions of $w$.
References
[1] The non-inversion sum of a permutation. St000341
Code
def statistic(w):
        return sum( b-a for a in range(len(w)) for b in range(a,len(w)) if w[a] < w[b] )

Created
Dec 26, 2015 at 14:39 by Christian Stump
Updated
Dec 26, 2015 at 14:39 by Christian Stump