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* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St000293
-----------------------------------------------------------------------------
Collection: Binary words
-----------------------------------------------------------------------------
Description: The number of inversions of a binary word.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(x):
return len(x.inversions())
-----------------------------------------------------------------------------
Statistic values:
0 => 0
1 => 0
00 => 0
01 => 0
10 => 1
11 => 0
000 => 0
001 => 0
010 => 1
011 => 0
100 => 2
101 => 1
110 => 2
111 => 0
0000 => 0
0001 => 0
0010 => 1
0011 => 0
0100 => 2
0101 => 1
0110 => 2
0111 => 0
1000 => 3
1001 => 2
1010 => 3
1011 => 1
1100 => 4
1101 => 2
1110 => 3
1111 => 0
00000 => 0
00001 => 0
00010 => 1
00011 => 0
00100 => 2
00101 => 1
00110 => 2
00111 => 0
01000 => 3
01001 => 2
01010 => 3
01011 => 1
01100 => 4
01101 => 2
01110 => 3
01111 => 0
10000 => 4
10001 => 3
10010 => 4
10011 => 2
10100 => 5
10101 => 3
10110 => 4
10111 => 1
11000 => 6
11001 => 4
11010 => 5
11011 => 2
11100 => 6
11101 => 3
11110 => 4
11111 => 0
000000 => 0
000001 => 0
000010 => 1
000011 => 0
000100 => 2
000101 => 1
000110 => 2
000111 => 0
001000 => 3
001001 => 2
001010 => 3
001011 => 1
001100 => 4
001101 => 2
001110 => 3
001111 => 0
010000 => 4
010001 => 3
010010 => 4
010011 => 2
010100 => 5
010101 => 3
010110 => 4
010111 => 1
011000 => 6
011001 => 4
011010 => 5
011011 => 2
011100 => 6
011101 => 3
011110 => 4
011111 => 0
100000 => 5
100001 => 4
100010 => 5
100011 => 3
100100 => 6
100101 => 4
100110 => 5
100111 => 2
101000 => 7
101001 => 5
101010 => 6
101011 => 3
101100 => 7
101101 => 4
101110 => 5
101111 => 1
110000 => 8
110001 => 6
110010 => 7
110011 => 4
110100 => 8
110101 => 5
110110 => 6
110111 => 2
111000 => 9
111001 => 6
111010 => 7
111011 => 3
111100 => 8
111101 => 4
111110 => 5
111111 => 0
0000000 => 0
0000001 => 0
0000010 => 1
0000011 => 0
0000100 => 2
0000101 => 1
0000110 => 2
0000111 => 0
0001000 => 3
0001001 => 2
0001010 => 3
0001011 => 1
0001100 => 4
0001101 => 2
0001110 => 3
0001111 => 0
0010000 => 4
0010001 => 3
0010010 => 4
0010011 => 2
0010100 => 5
0010101 => 3
0010110 => 4
0010111 => 1
0011000 => 6
0011001 => 4
0011010 => 5
0011011 => 2
0011100 => 6
0011101 => 3
0011110 => 4
0011111 => 0
0100000 => 5
0100001 => 4
0100010 => 5
0100011 => 3
0100100 => 6
0100101 => 4
0100110 => 5
0100111 => 2
0101000 => 7
0101001 => 5
0101010 => 6
0101011 => 3
0101100 => 7
0101101 => 4
0101110 => 5
0101111 => 1
0110000 => 8
0110001 => 6
0110010 => 7
0110011 => 4
0110100 => 8
0110101 => 5
0110110 => 6
0110111 => 2
0111000 => 9
0111001 => 6
0111010 => 7
0111011 => 3
0111100 => 8
0111101 => 4
0111110 => 5
0111111 => 0
1000000 => 6
1000001 => 5
1000010 => 6
1000011 => 4
1000100 => 7
1000101 => 5
1000110 => 6
1000111 => 3
1001000 => 8
1001001 => 6
1001010 => 7
1001011 => 4
1001100 => 8
1001101 => 5
1001110 => 6
1001111 => 2
1010000 => 9
1010001 => 7
1010010 => 8
1010011 => 5
1010100 => 9
1010101 => 6
1010110 => 7
1010111 => 3
1011000 => 10
1011001 => 7
1011010 => 8
1011011 => 4
1011100 => 9
1011101 => 5
1011110 => 6
1011111 => 1
1100000 => 10
1100001 => 8
1100010 => 9
1100011 => 6
1100100 => 10
1100101 => 7
1100110 => 8
1100111 => 4
1101000 => 11
1101001 => 8
1101010 => 9
1101011 => 5
1101100 => 10
1101101 => 6
1101110 => 7
1101111 => 2
1110000 => 12
1110001 => 9
1110010 => 10
1110011 => 6
1110100 => 11
1110101 => 7
1110110 => 8
1110111 => 3
1111000 => 12
1111001 => 8
1111010 => 9
1111011 => 4
1111100 => 10
1111101 => 5
1111110 => 6
1111111 => 0
00000000 => 0
00000001 => 0
00000010 => 1
00000011 => 0
00000100 => 2
00000101 => 1
00000110 => 2
00000111 => 0
00001000 => 3
00001001 => 2
00001010 => 3
00001011 => 1
00001100 => 4
00001101 => 2
00001110 => 3
00001111 => 0
00010000 => 4
00010001 => 3
00010010 => 4
00010011 => 2
00010100 => 5
00010101 => 3
00010110 => 4
00010111 => 1
00011000 => 6
00011001 => 4
00011010 => 5
00011011 => 2
00011100 => 6
00011101 => 3
00011110 => 4
00011111 => 0
00100000 => 5
00100001 => 4
00100010 => 5
00100011 => 3
00100100 => 6
00100101 => 4
00100110 => 5
00100111 => 2
00101000 => 7
00101001 => 5
00101010 => 6
00101011 => 3
00101100 => 7
00101101 => 4
00101110 => 5
00101111 => 1
00110000 => 8
00110001 => 6
00110010 => 7
00110011 => 4
00110100 => 8
00110101 => 5
00110110 => 6
00110111 => 2
00111000 => 9
00111001 => 6
00111010 => 7
00111011 => 3
00111100 => 8
00111101 => 4
00111110 => 5
00111111 => 0
01000000 => 6
01000001 => 5
01000010 => 6
01000011 => 4
01000100 => 7
01000101 => 5
01000110 => 6
01000111 => 3
01001000 => 8
01001001 => 6
01001010 => 7
01001011 => 4
01001100 => 8
01001101 => 5
01001110 => 6
01001111 => 2
01010000 => 9
01010001 => 7
01010010 => 8
01010011 => 5
01010100 => 9
01010101 => 6
01010110 => 7
01010111 => 3
01011000 => 10
01011001 => 7
01011010 => 8
01011011 => 4
01011100 => 9
01011101 => 5
01011110 => 6
01011111 => 1
01100000 => 10
01100001 => 8
01100010 => 9
01100011 => 6
01100100 => 10
01100101 => 7
01100110 => 8
01100111 => 4
01101000 => 11
01101001 => 8
01101010 => 9
01101011 => 5
01101100 => 10
01101101 => 6
01101110 => 7
01101111 => 2
01110000 => 12
01110001 => 9
01110010 => 10
01110011 => 6
01110100 => 11
01110101 => 7
01110110 => 8
01110111 => 3
01111000 => 12
01111001 => 8
01111010 => 9
01111011 => 4
01111100 => 10
01111101 => 5
01111110 => 6
01111111 => 0
10000000 => 7
10000001 => 6
10000010 => 7
10000011 => 5
10000100 => 8
10000101 => 6
10000110 => 7
10000111 => 4
10001000 => 9
10001001 => 7
10001010 => 8
10001011 => 5
10001100 => 9
10001101 => 6
10001110 => 7
10001111 => 3
10010000 => 10
10010001 => 8
10010010 => 9
10010011 => 6
10010100 => 10
10010101 => 7
10010110 => 8
10010111 => 4
10011000 => 11
10011001 => 8
10011010 => 9
10011011 => 5
10011100 => 10
10011101 => 6
10011110 => 7
10011111 => 2
10100000 => 11
10100001 => 9
10100010 => 10
10100011 => 7
10100100 => 11
10100101 => 8
10100110 => 9
10100111 => 5
10101000 => 12
10101001 => 9
10101010 => 10
10101011 => 6
10101100 => 11
10101101 => 7
10101110 => 8
10101111 => 3
10110000 => 13
10110001 => 10
10110010 => 11
10110011 => 7
10110100 => 12
10110101 => 8
10110110 => 9
10110111 => 4
10111000 => 13
10111001 => 9
10111010 => 10
10111011 => 5
10111100 => 11
10111101 => 6
10111110 => 7
10111111 => 1
11000000 => 12
11000001 => 10
11000010 => 11
11000011 => 8
11000100 => 12
11000101 => 9
11000110 => 10
11000111 => 6
11001000 => 13
11001001 => 10
11001010 => 11
11001011 => 7
11001100 => 12
11001101 => 8
11001110 => 9
11001111 => 4
11010000 => 14
11010001 => 11
11010010 => 12
11010011 => 8
11010100 => 13
11010101 => 9
11010110 => 10
11010111 => 5
11011000 => 14
11011001 => 10
11011010 => 11
11011011 => 6
11011100 => 12
11011101 => 7
11011110 => 8
11011111 => 2
11100000 => 15
11100001 => 12
11100010 => 13
11100011 => 9
11100100 => 14
11100101 => 10
11100110 => 11
11100111 => 6
11101000 => 15
11101001 => 11
11101010 => 12
11101011 => 7
11101100 => 13
11101101 => 8
11101110 => 9
11101111 => 3
11110000 => 16
11110001 => 12
11110010 => 13
11110011 => 8
11110100 => 14
11110101 => 9
11110110 => 10
11110111 => 4
11111000 => 15
11111001 => 10
11111010 => 11
11111011 => 5
11111100 => 12
11111101 => 6
11111110 => 7
11111111 => 0
000000000 => 0
000000001 => 0
000000010 => 1
000000011 => 0
000000100 => 2
000000101 => 1
000000110 => 2
000000111 => 0
000001000 => 3
000001001 => 2
000001010 => 3
000001011 => 1
000001100 => 4
000001101 => 2
000001110 => 3
000001111 => 0
000010000 => 4
000010001 => 3
000010010 => 4
000010011 => 2
000010100 => 5
000010101 => 3
000010110 => 4
000010111 => 1
000011000 => 6
000011001 => 4
000011010 => 5
000011011 => 2
000011100 => 6
000011101 => 3
000011110 => 4
000011111 => 0
000100000 => 5
000100001 => 4
000100010 => 5
000100011 => 3
000100100 => 6
000100101 => 4
000100110 => 5
000100111 => 2
000101000 => 7
000101001 => 5
000101010 => 6
000101011 => 3
000101100 => 7
000101101 => 4
000101110 => 5
000101111 => 1
000110000 => 8
000110001 => 6
000110010 => 7
000110011 => 4
000110100 => 8
000110101 => 5
000110110 => 6
000110111 => 2
000111000 => 9
000111001 => 6
000111010 => 7
000111011 => 3
000111100 => 8
000111101 => 4
000111110 => 5
000111111 => 0
001000000 => 6
001000001 => 5
001000010 => 6
001000011 => 4
001000100 => 7
001000101 => 5
001000110 => 6
001000111 => 3
001001000 => 8
001001001 => 6
001001010 => 7
001001011 => 4
001001100 => 8
001001101 => 5
001001110 => 6
001001111 => 2
001010000 => 9
001010001 => 7
001010010 => 8
001010011 => 5
001010100 => 9
001010101 => 6
001010110 => 7
001010111 => 3
001011000 => 10
001011001 => 7
001011010 => 8
001011011 => 4
001011100 => 9
001011101 => 5
001011110 => 6
001011111 => 1
001100000 => 10
001100001 => 8
001100010 => 9
001100011 => 6
001100100 => 10
001100101 => 7
001100110 => 8
001100111 => 4
001101000 => 11
001101001 => 8
001101010 => 9
001101011 => 5
001101100 => 10
001101101 => 6
001101110 => 7
001101111 => 2
001110000 => 12
001110001 => 9
001110010 => 10
001110011 => 6
001110100 => 11
001110101 => 7
001110110 => 8
001110111 => 3
001111000 => 12
001111001 => 8
001111010 => 9
001111011 => 4
001111100 => 10
001111101 => 5
001111110 => 6
001111111 => 0
010000000 => 7
010000001 => 6
010000010 => 7
010000011 => 5
010000100 => 8
010000101 => 6
010000110 => 7
010000111 => 4
010001000 => 9
010001001 => 7
010001010 => 8
010001011 => 5
010001100 => 9
010001101 => 6
010001110 => 7
010001111 => 3
010010000 => 10
010010001 => 8
010010010 => 9
010010011 => 6
010010100 => 10
010010101 => 7
010010110 => 8
010010111 => 4
010011000 => 11
010011001 => 8
010011010 => 9
010011011 => 5
010011100 => 10
010011101 => 6
010011110 => 7
010011111 => 2
010100000 => 11
010100001 => 9
010100010 => 10
010100011 => 7
010100100 => 11
010100101 => 8
010100110 => 9
010100111 => 5
010101000 => 12
010101001 => 9
010101010 => 10
010101011 => 6
010101100 => 11
010101101 => 7
010101110 => 8
010101111 => 3
010110000 => 13
010110001 => 10
010110010 => 11
010110011 => 7
010110100 => 12
010110101 => 8
010110110 => 9
010110111 => 4
010111000 => 13
010111001 => 9
010111010 => 10
010111011 => 5
010111100 => 11
010111101 => 6
010111110 => 7
010111111 => 1
011000000 => 12
011000001 => 10
011000010 => 11
011000011 => 8
011000100 => 12
011000101 => 9
011000110 => 10
011000111 => 6
011001000 => 13
011001001 => 10
011001010 => 11
011001011 => 7
011001100 => 12
011001101 => 8
011001110 => 9
011001111 => 4
011010000 => 14
011010001 => 11
011010010 => 12
011010011 => 8
011010100 => 13
011010101 => 9
011010110 => 10
011010111 => 5
011011000 => 14
011011001 => 10
011011010 => 11
011011011 => 6
011011100 => 12
011011101 => 7
011011110 => 8
011011111 => 2
011100000 => 15
011100001 => 12
011100010 => 13
011100011 => 9
011100100 => 14
011100101 => 10
011100110 => 11
011100111 => 6
011101000 => 15
011101001 => 11
011101010 => 12
011101011 => 7
011101100 => 13
011101101 => 8
011101110 => 9
011101111 => 3
011110000 => 16
011110001 => 12
011110010 => 13
011110011 => 8
011110100 => 14
011110101 => 9
011110110 => 10
011110111 => 4
011111000 => 15
011111001 => 10
011111010 => 11
011111011 => 5
011111100 => 12
011111101 => 6
011111110 => 7
011111111 => 0
100000000 => 8
100000001 => 7
100000010 => 8
100000011 => 6
100000100 => 9
100000101 => 7
100000110 => 8
100000111 => 5
100001000 => 10
100001001 => 8
100001010 => 9
100001011 => 6
100001100 => 10
100001101 => 7
100001110 => 8
100001111 => 4
100010000 => 11
100010001 => 9
100010010 => 10
100010011 => 7
100010100 => 11
100010101 => 8
100010110 => 9
100010111 => 5
100011000 => 12
100011001 => 9
100011010 => 10
100011011 => 6
100011100 => 11
100011101 => 7
100011110 => 8
100011111 => 3
100100000 => 12
100100001 => 10
100100010 => 11
100100011 => 8
100100100 => 12
100100101 => 9
100100110 => 10
100100111 => 6
100101000 => 13
100101001 => 10
100101010 => 11
100101011 => 7
100101100 => 12
100101101 => 8
100101110 => 9
100101111 => 4
100110000 => 14
100110001 => 11
100110010 => 12
100110011 => 8
100110100 => 13
100110101 => 9
100110110 => 10
100110111 => 5
100111000 => 14
100111001 => 10
100111010 => 11
100111011 => 6
100111100 => 12
100111101 => 7
100111110 => 8
100111111 => 2
101000000 => 13
101000001 => 11
101000010 => 12
101000011 => 9
101000100 => 13
101000101 => 10
101000110 => 11
101000111 => 7
101001000 => 14
101001001 => 11
101001010 => 12
101001011 => 8
101001100 => 13
101001101 => 9
101001110 => 10
101001111 => 5
101010000 => 15
101010001 => 12
101010010 => 13
101010011 => 9
101010100 => 14
101010101 => 10
101010110 => 11
101010111 => 6
101011000 => 15
101011001 => 11
101011010 => 12
101011011 => 7
101011100 => 13
101011101 => 8
101011110 => 9
101011111 => 3
101100000 => 16
101100001 => 13
101100010 => 14
101100011 => 10
101100100 => 15
101100101 => 11
101100110 => 12
101100111 => 7
101101000 => 16
101101001 => 12
101101010 => 13
101101011 => 8
101101100 => 14
101101101 => 9
101101110 => 10
101101111 => 4
101110000 => 17
101110001 => 13
101110010 => 14
101110011 => 9
101110100 => 15
101110101 => 10
101110110 => 11
101110111 => 5
101111000 => 16
101111001 => 11
101111010 => 12
101111011 => 6
101111100 => 13
101111101 => 7
101111110 => 8
101111111 => 1
110000000 => 14
110000001 => 12
110000010 => 13
110000011 => 10
110000100 => 14
110000101 => 11
110000110 => 12
110000111 => 8
110001000 => 15
110001001 => 12
110001010 => 13
110001011 => 9
110001100 => 14
110001101 => 10
110001110 => 11
110001111 => 6
110010000 => 16
110010001 => 13
110010010 => 14
110010011 => 10
110010100 => 15
110010101 => 11
110010110 => 12
110010111 => 7
110011000 => 16
110011001 => 12
110011010 => 13
110011011 => 8
110011100 => 14
110011101 => 9
110011110 => 10
110011111 => 4
110100000 => 17
110100001 => 14
110100010 => 15
110100011 => 11
110100100 => 16
110100101 => 12
110100110 => 13
110100111 => 8
110101000 => 17
110101001 => 13
110101010 => 14
110101011 => 9
110101100 => 15
110101101 => 10
110101110 => 11
110101111 => 5
110110000 => 18
110110001 => 14
110110010 => 15
110110011 => 10
110110100 => 16
110110101 => 11
110110110 => 12
110110111 => 6
110111000 => 17
110111001 => 12
110111010 => 13
110111011 => 7
110111100 => 14
110111101 => 8
110111110 => 9
110111111 => 2
111000000 => 18
111000001 => 15
111000010 => 16
111000011 => 12
111000100 => 17
111000101 => 13
111000110 => 14
111000111 => 9
111001000 => 18
111001001 => 14
111001010 => 15
111001011 => 10
111001100 => 16
111001101 => 11
111001110 => 12
111001111 => 6
111010000 => 19
111010001 => 15
111010010 => 16
111010011 => 11
111010100 => 17
111010101 => 12
111010110 => 13
111010111 => 7
111011000 => 18
111011001 => 13
111011010 => 14
111011011 => 8
111011100 => 15
111011101 => 9
111011110 => 10
111011111 => 3
111100000 => 20
111100001 => 16
111100010 => 17
111100011 => 12
111100100 => 18
111100101 => 13
111100110 => 14
111100111 => 8
111101000 => 19
111101001 => 14
111101010 => 15
111101011 => 9
111101100 => 16
111101101 => 10
111101110 => 11
111101111 => 4
111110000 => 20
111110001 => 15
111110010 => 16
111110011 => 10
111110100 => 17
111110101 => 11
111110110 => 12
111110111 => 5
111111000 => 18
111111001 => 12
111111010 => 13
111111011 => 6
111111100 => 14
111111101 => 7
111111110 => 8
111111111 => 0
1010101010 => 15
1010101100 => 16
1010110010 => 16
1010110100 => 17
1010111000 => 18
1011001010 => 16
1011001100 => 17
1011010010 => 17
1011010100 => 18
1011011000 => 19
1011100010 => 18
1011100100 => 19
1011101000 => 20
1011110000 => 21
1100101010 => 16
1100101100 => 17
1100110010 => 17
1100110100 => 18
1100111000 => 19
1101001010 => 17
1101001100 => 18
1101010010 => 18
1101010100 => 19
1101011000 => 20
1101100010 => 19
1101100100 => 20
1101101000 => 21
1101110000 => 22
1110001010 => 18
1110001100 => 19
1110010010 => 19
1110010100 => 20
1110011000 => 21
1110100010 => 20
1110100100 => 21
1110101000 => 22
1110110000 => 23
1111000010 => 21
1111000100 => 22
1111001000 => 23
1111010000 => 24
1111100000 => 25
1111111110 => 9
1111111101 => 8
1111000001 => 20
1110111110 => 11
1110100001 => 19
1110011110 => 13
1110010001 => 18
1110001001 => 17
1110000101 => 16
1101111110 => 10
1101100001 => 18
1101010001 => 17
1101001110 => 14
1101001001 => 16
1101000101 => 15
1100110001 => 16
1100101001 => 15
1100100110 => 15
1100100101 => 14
1100011001 => 14
1100010101 => 13
1100010010 => 16
1100001000 => 17
1011111110 => 9
1011111101 => 8
1011100001 => 17
1011010001 => 16
1011001001 => 15
1011000101 => 14
1010111110 => 10
1010110001 => 15
1010101001 => 14
1010100110 => 14
1010100101 => 13
1010011010 => 14
1010011001 => 13
1010010110 => 13
1010010101 => 12
1010001110 => 12
1001111110 => 9
1001111000 => 17
1001110100 => 16
1001110001 => 14
1001101100 => 15
1001101010 => 14
1001101001 => 13
1001100110 => 13
1001100101 => 12
1001011110 => 10
1001011010 => 13
1001011001 => 12
1001010110 => 12
1001010101 => 11
1001001110 => 11
1000111110 => 9
1000111100 => 13
1000111010 => 12
1000110110 => 11
1000101110 => 10
1000011110 => 9
1000010110 => 10
1000001110 => 9
1000001010 => 10
1000000110 => 9
1000000100 => 10
1000000010 => 9
1000000000 => 9
0111111111 => 0
0111111101 => 7
0111111001 => 12
0111110001 => 15
0111100001 => 16
0111000001 => 15
0110000001 => 12
0100000001 => 7
0000000001 => 0
0111111011 => 6
0111110101 => 11
0111101001 => 14
0111010001 => 15
0110100001 => 14
0101000001 => 11
0010000001 => 6
0101010101 => 10
0101010011 => 9
0101001101 => 9
0101001011 => 8
0101000111 => 7
0100110101 => 9
0100110011 => 8
0100101101 => 8
0100101011 => 7
0100100111 => 6
0100011101 => 7
0100011011 => 6
0100010111 => 5
0100001111 => 4
0011010101 => 9
0011010011 => 8
0011001101 => 8
0011001011 => 7
0011000111 => 6
0010110101 => 8
0010110011 => 7
0010101101 => 7
0010101011 => 6
0010100111 => 5
0010011101 => 6
0010011011 => 5
0010010111 => 4
0010001111 => 3
0001110101 => 7
0001110011 => 6
0001101101 => 6
0001101011 => 5
0001100111 => 4
0001011101 => 5
0001011011 => 4
0001010111 => 3
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-----------------------------------------------------------------------------
Created: Nov 19, 2015 at 12:14 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Feb 12, 2018 at 22:30 by Martin Rubey