Identifier
-
Mp00316:
Binary words
—inverse Foata bijection⟶
Binary words
St000290: Binary words ⟶ ℤ
Values
=>
0=>0=>0
1=>1=>0
00=>00=>0
01=>01=>0
10=>10=>1
11=>11=>0
000=>000=>0
001=>001=>0
010=>100=>1
011=>011=>0
100=>010=>2
101=>101=>1
110=>110=>2
111=>111=>0
0000=>0000=>0
0001=>0001=>0
0010=>1000=>1
0011=>0011=>0
0100=>0100=>2
0101=>1001=>1
0110=>1100=>2
0111=>0111=>0
1000=>0010=>3
1001=>0101=>2
1010=>0110=>3
1011=>1011=>1
1100=>1010=>4
1101=>1101=>2
1110=>1110=>3
1111=>1111=>0
00000=>00000=>0
00001=>00001=>0
00010=>10000=>1
00011=>00011=>0
00100=>01000=>2
00101=>10001=>1
00110=>11000=>2
00111=>00111=>0
01000=>00100=>3
01001=>01001=>2
01010=>01100=>3
01011=>10011=>1
01100=>10100=>4
01101=>11001=>2
01110=>11100=>3
01111=>01111=>0
10000=>00010=>4
10001=>00101=>3
10010=>00110=>4
10011=>01011=>2
10100=>10010=>5
10101=>01101=>3
10110=>01110=>4
10111=>10111=>1
11000=>01010=>6
11001=>10101=>4
11010=>10110=>5
11011=>11011=>2
11100=>11010=>6
11101=>11101=>3
11110=>11110=>4
11111=>11111=>0
000000=>000000=>0
000001=>000001=>0
000010=>100000=>1
000011=>000011=>0
000100=>010000=>2
000101=>100001=>1
000110=>110000=>2
000111=>000111=>0
001000=>001000=>3
001001=>010001=>2
001010=>011000=>3
001011=>100011=>1
001100=>101000=>4
001101=>110001=>2
001110=>111000=>3
001111=>001111=>0
010000=>000100=>4
010001=>001001=>3
010010=>001100=>4
010011=>010011=>2
010100=>100100=>5
010101=>011001=>3
010110=>011100=>4
010111=>100111=>1
011000=>010100=>6
011001=>101001=>4
011010=>101100=>5
011011=>110011=>2
011100=>110100=>6
011101=>111001=>3
011110=>111100=>4
011111=>011111=>0
100000=>000010=>5
100001=>000101=>4
100010=>000110=>5
100011=>001011=>3
100100=>100010=>6
100101=>001101=>4
100110=>001110=>5
100111=>010111=>2
101000=>010010=>7
101001=>100101=>5
101010=>100110=>6
101011=>011011=>3
101100=>110010=>7
101101=>011101=>4
101110=>011110=>5
101111=>101111=>1
110000=>001010=>8
110001=>010101=>6
110010=>010110=>7
110011=>101011=>4
110100=>011010=>8
110101=>101101=>5
110110=>101110=>6
110111=>110111=>2
111000=>101010=>9
111001=>110101=>6
111010=>110110=>7
111011=>111011=>3
111100=>111010=>8
111101=>111101=>4
111110=>111110=>5
111111=>111111=>0
0000000=>0000000=>0
0000001=>0000001=>0
0000010=>1000000=>1
0000011=>0000011=>0
0000100=>0100000=>2
0000101=>1000001=>1
0000110=>1100000=>2
0000111=>0000111=>0
0001000=>0010000=>3
0001001=>0100001=>2
0001010=>0110000=>3
0001011=>1000011=>1
0001100=>1010000=>4
0001101=>1100001=>2
0001110=>1110000=>3
0001111=>0001111=>0
0010000=>0001000=>4
0010001=>0010001=>3
0010010=>0011000=>4
0010011=>0100011=>2
0010100=>1001000=>5
0010101=>0110001=>3
0010110=>0111000=>4
0010111=>1000111=>1
0011000=>0101000=>6
0011001=>1010001=>4
0011010=>1011000=>5
0011011=>1100011=>2
0011100=>1101000=>6
0011101=>1110001=>3
0011110=>1111000=>4
0011111=>0011111=>0
0100000=>0000100=>5
0100001=>0001001=>4
0100010=>0001100=>5
0100011=>0010011=>3
0100100=>1000100=>6
0100101=>0011001=>4
0100110=>0011100=>5
0100111=>0100111=>2
0101000=>0100100=>7
0101001=>1001001=>5
0101010=>1001100=>6
0101011=>0110011=>3
0101100=>1100100=>7
0101101=>0111001=>4
0101110=>0111100=>5
0101111=>1001111=>1
0110000=>0010100=>8
0110001=>0101001=>6
0110010=>0101100=>7
0110011=>1010011=>4
0110100=>0110100=>8
0110101=>1011001=>5
0110110=>1011100=>6
0110111=>1100111=>2
0111000=>1010100=>9
0111001=>1101001=>6
0111010=>1101100=>7
0111011=>1110011=>3
0111100=>1110100=>8
0111101=>1111001=>4
0111110=>1111100=>5
0111111=>0111111=>0
1000000=>0000010=>6
1000001=>0000101=>5
1000010=>0000110=>6
1000011=>0001011=>4
1000100=>1000010=>7
1000101=>0001101=>5
1000110=>0001110=>6
1000111=>0010111=>3
1001000=>0100010=>8
1001001=>1000101=>6
1001010=>1000110=>7
1001011=>0011011=>4
1001100=>1100010=>8
1001101=>0011101=>5
1001110=>0011110=>6
1001111=>0101111=>2
1010000=>0010010=>9
1010001=>0100101=>7
1010010=>0100110=>8
1010011=>1001011=>5
1010100=>0110010=>9
1010101=>1001101=>6
1010110=>1001110=>7
1010111=>0110111=>3
1011000=>1010010=>10
1011001=>1100101=>7
1011010=>1100110=>8
1011011=>0111011=>4
1011100=>1110010=>9
1011101=>0111101=>5
1011110=>0111110=>6
1011111=>1011111=>1
1100000=>0001010=>10
1100001=>0010101=>8
1100010=>0010110=>9
1100011=>0101011=>6
1100100=>0011010=>10
1100101=>0101101=>7
1100110=>0101110=>8
1100111=>1010111=>4
1101000=>1001010=>11
1101001=>0110101=>8
1101010=>0110110=>9
1101011=>1011011=>5
1101100=>0111010=>10
1101101=>1011101=>6
1101110=>1011110=>7
1101111=>1101111=>2
1110000=>0101010=>12
1110001=>1010101=>9
1110010=>1010110=>10
1110011=>1101011=>6
1110100=>1011010=>11
1110101=>1101101=>7
1110110=>1101110=>8
1110111=>1110111=>3
1111000=>1101010=>12
1111001=>1110101=>8
1111010=>1110110=>9
1111011=>1111011=>4
1111100=>1111010=>10
1111101=>1111101=>5
1111110=>1111110=>6
1111111=>1111111=>0
00000000=>00000000=>0
00000001=>00000001=>0
00000010=>10000000=>1
00000011=>00000011=>0
00000100=>01000000=>2
00000101=>10000001=>1
00000110=>11000000=>2
00000111=>00000111=>0
00001000=>00100000=>3
00001001=>01000001=>2
00001010=>01100000=>3
00001011=>10000011=>1
00001100=>10100000=>4
00001101=>11000001=>2
00001110=>11100000=>3
00001111=>00001111=>0
00010000=>00010000=>4
00010001=>00100001=>3
00010010=>00110000=>4
00010011=>01000011=>2
00010100=>10010000=>5
00010101=>01100001=>3
00010110=>01110000=>4
00010111=>10000111=>1
00011000=>01010000=>6
00011001=>10100001=>4
00011010=>10110000=>5
00011011=>11000011=>2
00011100=>11010000=>6
00011101=>11100001=>3
00011110=>11110000=>4
00011111=>00011111=>0
00100000=>00001000=>5
00100001=>00010001=>4
00100010=>00011000=>5
00100011=>00100011=>3
00100100=>10001000=>6
00100101=>00110001=>4
00100110=>00111000=>5
00100111=>01000111=>2
00101000=>01001000=>7
00101001=>10010001=>5
00101010=>10011000=>6
00101011=>01100011=>3
00101100=>11001000=>7
00101101=>01110001=>4
00101110=>01111000=>5
00101111=>10001111=>1
00110000=>00101000=>8
00110001=>01010001=>6
00110010=>01011000=>7
00110011=>10100011=>4
00110100=>01101000=>8
00110101=>10110001=>5
00110110=>10111000=>6
00110111=>11000111=>2
00111000=>10101000=>9
00111001=>11010001=>6
00111010=>11011000=>7
00111011=>11100011=>3
00111100=>11101000=>8
00111101=>11110001=>4
00111110=>11111000=>5
00111111=>00111111=>0
01000000=>00000100=>6
01000001=>00001001=>5
01000010=>00001100=>6
01000011=>00010011=>4
01000100=>10000100=>7
01000101=>00011001=>5
01000110=>00011100=>6
01000111=>00100111=>3
01001000=>01000100=>8
01001001=>10001001=>6
01001010=>10001100=>7
01001011=>00110011=>4
01001100=>11000100=>8
01001101=>00111001=>5
01001110=>00111100=>6
01001111=>01001111=>2
01010000=>00100100=>9
01010001=>01001001=>7
01010010=>01001100=>8
01010011=>10010011=>5
01010100=>01100100=>9
01010101=>10011001=>6
01010110=>10011100=>7
01010111=>01100111=>3
01011000=>10100100=>10
01011001=>11001001=>7
01011010=>11001100=>8
01011011=>01110011=>4
01011100=>11100100=>9
01011101=>01111001=>5
01011110=>01111100=>6
01011111=>10011111=>1
01100000=>00010100=>10
01100001=>00101001=>8
01100010=>00101100=>9
01100011=>01010011=>6
01100100=>00110100=>10
01100101=>01011001=>7
01100110=>01011100=>8
01100111=>10100111=>4
01101000=>10010100=>11
01101001=>01101001=>8
01101010=>01101100=>9
01101011=>10110011=>5
01101100=>01110100=>10
01101101=>10111001=>6
01101110=>10111100=>7
01101111=>11001111=>2
01110000=>01010100=>12
01110001=>10101001=>9
01110010=>10101100=>10
01110011=>11010011=>6
01110100=>10110100=>11
01110101=>11011001=>7
01110110=>11011100=>8
01110111=>11100111=>3
01111000=>11010100=>12
01111001=>11101001=>8
01111010=>11101100=>9
01111011=>11110011=>4
01111100=>11110100=>10
01111101=>11111001=>5
01111110=>11111100=>6
01111111=>01111111=>0
10000000=>00000010=>7
10000001=>00000101=>6
10000010=>00000110=>7
10000011=>00001011=>5
10000100=>10000010=>8
10000101=>00001101=>6
10000110=>00001110=>7
10000111=>00010111=>4
10001000=>01000010=>9
10001001=>10000101=>7
10001010=>10000110=>8
10001011=>00011011=>5
10001100=>11000010=>9
10001101=>00011101=>6
10001110=>00011110=>7
10001111=>00101111=>3
10010000=>00100010=>10
10010001=>01000101=>8
10010010=>01000110=>9
10010011=>10001011=>6
10010100=>01100010=>10
10010101=>10001101=>7
10010110=>10001110=>8
10010111=>00110111=>4
10011000=>10100010=>11
10011001=>11000101=>8
10011010=>11000110=>9
10011011=>00111011=>5
10011100=>11100010=>10
10011101=>00111101=>6
10011110=>00111110=>7
10011111=>01011111=>2
10100000=>00010010=>11
10100001=>00100101=>9
10100010=>00100110=>10
10100011=>01001011=>7
10100100=>00110010=>11
10100101=>01001101=>8
10100110=>01001110=>9
10100111=>10010111=>5
10101000=>10010010=>12
10101001=>01100101=>9
10101010=>01100110=>10
10101011=>10011011=>6
10101100=>01110010=>11
10101101=>10011101=>7
10101110=>10011110=>8
10101111=>01101111=>3
10110000=>01010010=>13
10110001=>10100101=>10
10110010=>10100110=>11
10110011=>11001011=>7
10110100=>10110010=>12
10110101=>11001101=>8
10110110=>11001110=>9
10110111=>01110111=>4
10111000=>11010010=>13
10111001=>11100101=>9
10111010=>11100110=>10
10111011=>01111011=>5
10111100=>11110010=>11
10111101=>01111101=>6
10111110=>01111110=>7
10111111=>10111111=>1
11000000=>00001010=>12
11000001=>00010101=>10
11000010=>00010110=>11
11000011=>00101011=>8
11000100=>00011010=>12
11000101=>00101101=>9
11000110=>00101110=>10
11000111=>01010111=>6
11001000=>10001010=>13
11001001=>00110101=>10
11001010=>00110110=>11
11001011=>01011011=>7
11001100=>00111010=>12
11001101=>01011101=>8
11001110=>01011110=>9
11001111=>10101111=>4
11010000=>01001010=>14
11010001=>10010101=>11
11010010=>10010110=>12
11010011=>01101011=>8
11010100=>10011010=>13
11010101=>01101101=>9
11010110=>01101110=>10
11010111=>10110111=>5
11011000=>11001010=>14
11011001=>01110101=>10
11011010=>01110110=>11
11011011=>10111011=>6
11011100=>01111010=>12
11011101=>10111101=>7
11011110=>10111110=>8
11011111=>11011111=>2
11100000=>00101010=>15
11100001=>01010101=>12
11100010=>01010110=>13
11100011=>10101011=>9
11100100=>01011010=>14
11100101=>10101101=>10
11100110=>10101110=>11
11100111=>11010111=>6
11101000=>01101010=>15
11101001=>10110101=>11
11101010=>10110110=>12
11101011=>11011011=>7
11101100=>10111010=>13
11101101=>11011101=>8
11101110=>11011110=>9
11101111=>11101111=>3
11110000=>10101010=>16
11110001=>11010101=>12
11110010=>11010110=>13
11110011=>11101011=>8
11110100=>11011010=>14
11110101=>11101101=>9
11110110=>11101110=>10
11110111=>11110111=>4
11111000=>11101010=>15
11111001=>11110101=>10
11111010=>11110110=>11
11111011=>11111011=>5
11111100=>11111010=>12
11111101=>11111101=>6
11111110=>11111110=>7
11111111=>11111111=>0
000000000=>000000000=>0
000000001=>000000001=>0
000000010=>100000000=>1
000000011=>000000011=>0
000000100=>010000000=>2
000000101=>100000001=>1
000000110=>110000000=>2
000000111=>000000111=>0
000001000=>001000000=>3
000001001=>010000001=>2
000001010=>011000000=>3
000001011=>100000011=>1
000001100=>101000000=>4
000001101=>110000001=>2
000001110=>111000000=>3
000001111=>000001111=>0
000010000=>000100000=>4
000010001=>001000001=>3
000010010=>001100000=>4
000010011=>010000011=>2
000010100=>100100000=>5
000010101=>011000001=>3
000010110=>011100000=>4
000010111=>100000111=>1
000011000=>010100000=>6
000011001=>101000001=>4
000011010=>101100000=>5
000011011=>110000011=>2
000011100=>110100000=>6
000011101=>111000001=>3
000011110=>111100000=>4
000011111=>000011111=>0
000100000=>000010000=>5
000100001=>000100001=>4
000100010=>000110000=>5
000100011=>001000011=>3
000100100=>100010000=>6
000100101=>001100001=>4
000100110=>001110000=>5
000100111=>010000111=>2
000101000=>010010000=>7
000101001=>100100001=>5
000101010=>100110000=>6
000101011=>011000011=>3
000101100=>110010000=>7
000101101=>011100001=>4
000101110=>011110000=>5
000101111=>100001111=>1
000110000=>001010000=>8
000110001=>010100001=>6
000110010=>010110000=>7
000110011=>101000011=>4
000110100=>011010000=>8
000110101=>101100001=>5
000110110=>101110000=>6
000110111=>110000111=>2
000111000=>101010000=>9
000111001=>110100001=>6
000111010=>110110000=>7
000111011=>111000011=>3
000111100=>111010000=>8
000111101=>111100001=>4
000111110=>111110000=>5
000111111=>000111111=>0
001000000=>000001000=>6
001000001=>000010001=>5
001000010=>000011000=>6
001000011=>000100011=>4
001000100=>100001000=>7
001000101=>000110001=>5
001000110=>000111000=>6
001000111=>001000111=>3
001001000=>010001000=>8
001001001=>100010001=>6
001001010=>100011000=>7
001001011=>001100011=>4
001001100=>110001000=>8
001001101=>001110001=>5
001001110=>001111000=>6
001001111=>010001111=>2
001010000=>001001000=>9
001010001=>010010001=>7
001010010=>010011000=>8
001010011=>100100011=>5
001010100=>011001000=>9
001010101=>100110001=>6
001010110=>100111000=>7
001010111=>011000111=>3
001011000=>101001000=>10
001011001=>110010001=>7
001011010=>110011000=>8
001011011=>011100011=>4
001011100=>111001000=>9
001011101=>011110001=>5
001011110=>011111000=>6
001011111=>100011111=>1
001100000=>000101000=>10
001100001=>001010001=>8
001100010=>001011000=>9
001100011=>010100011=>6
001100100=>001101000=>10
001100101=>010110001=>7
001100110=>010111000=>8
001100111=>101000111=>4
001101000=>100101000=>11
001101001=>011010001=>8
001101010=>011011000=>9
001101011=>101100011=>5
001101100=>011101000=>10
001101101=>101110001=>6
001101110=>101111000=>7
001101111=>110001111=>2
001110000=>010101000=>12
001110001=>101010001=>9
001110010=>101011000=>10
001110011=>110100011=>6
001110100=>101101000=>11
001110101=>110110001=>7
001110110=>110111000=>8
001110111=>111000111=>3
001111000=>110101000=>12
001111001=>111010001=>8
001111010=>111011000=>9
001111011=>111100011=>4
001111100=>111101000=>10
001111101=>111110001=>5
001111110=>111111000=>6
001111111=>001111111=>0
010000000=>000000100=>7
010000001=>000001001=>6
010000010=>000001100=>7
010000011=>000010011=>5
010000100=>100000100=>8
010000101=>000011001=>6
010000110=>000011100=>7
010000111=>000100111=>4
010001000=>010000100=>9
010001001=>100001001=>7
010001010=>100001100=>8
010001011=>000110011=>5
010001100=>110000100=>9
010001101=>000111001=>6
010001110=>000111100=>7
010001111=>001001111=>3
010010000=>001000100=>10
010010001=>010001001=>8
010010010=>010001100=>9
010010011=>100010011=>6
010010100=>011000100=>10
010010101=>100011001=>7
010010110=>100011100=>8
010010111=>001100111=>4
010011000=>101000100=>11
010011001=>110001001=>8
010011010=>110001100=>9
010011011=>001110011=>5
010011100=>111000100=>10
010011101=>001111001=>6
010011110=>001111100=>7
010011111=>010011111=>2
010100000=>000100100=>11
010100001=>001001001=>9
010100010=>001001100=>10
010100011=>010010011=>7
010100100=>001100100=>11
010100101=>010011001=>8
010100110=>010011100=>9
010100111=>100100111=>5
010101000=>100100100=>12
010101001=>011001001=>9
010101010=>011001100=>10
010101011=>100110011=>6
010101100=>011100100=>11
010101101=>100111001=>7
010101110=>100111100=>8
010101111=>011001111=>3
010110000=>010100100=>13
010110001=>101001001=>10
010110010=>101001100=>11
010110011=>110010011=>7
010110100=>101100100=>12
010110101=>110011001=>8
010110110=>110011100=>9
010110111=>011100111=>4
010111000=>110100100=>13
010111001=>111001001=>9
010111010=>111001100=>10
010111011=>011110011=>5
010111100=>111100100=>11
010111101=>011111001=>6
010111110=>011111100=>7
010111111=>100111111=>1
011000000=>000010100=>12
011000001=>000101001=>10
011000010=>000101100=>11
011000011=>001010011=>8
011000100=>000110100=>12
011000101=>001011001=>9
011000110=>001011100=>10
011000111=>010100111=>6
011001000=>100010100=>13
011001001=>001101001=>10
011001010=>001101100=>11
011001011=>010110011=>7
011001100=>001110100=>12
011001101=>010111001=>8
011001110=>010111100=>9
011001111=>101001111=>4
011010000=>010010100=>14
011010001=>100101001=>11
011010010=>100101100=>12
011010011=>011010011=>8
011010100=>100110100=>13
011010101=>011011001=>9
011010110=>011011100=>10
011010111=>101100111=>5
011011000=>110010100=>14
011011001=>011101001=>10
011011010=>011101100=>11
011011011=>101110011=>6
011011100=>011110100=>12
011011101=>101111001=>7
011011110=>101111100=>8
011011111=>110011111=>2
011100000=>001010100=>15
011100001=>010101001=>12
011100010=>010101100=>13
011100011=>101010011=>9
011100100=>010110100=>14
011100101=>101011001=>10
011100110=>101011100=>11
011100111=>110100111=>6
011101000=>011010100=>15
011101001=>101101001=>11
011101010=>101101100=>12
011101011=>110110011=>7
011101100=>101110100=>13
011101101=>110111001=>8
011101110=>110111100=>9
011101111=>111001111=>3
011110000=>101010100=>16
011110001=>110101001=>12
011110010=>110101100=>13
011110011=>111010011=>8
011110100=>110110100=>14
011110101=>111011001=>9
011110110=>111011100=>10
011110111=>111100111=>4
011111000=>111010100=>15
011111001=>111101001=>10
011111010=>111101100=>11
011111011=>111110011=>5
011111100=>111110100=>12
011111101=>111111001=>6
011111110=>111111100=>7
011111111=>011111111=>0
100000000=>000000010=>8
100000001=>000000101=>7
100000010=>000000110=>8
100000011=>000001011=>6
100000100=>100000010=>9
100000101=>000001101=>7
100000110=>000001110=>8
100000111=>000010111=>5
100001000=>010000010=>10
100001001=>100000101=>8
100001010=>100000110=>9
100001011=>000011011=>6
100001100=>110000010=>10
100001101=>000011101=>7
100001110=>000011110=>8
100001111=>000101111=>4
100010000=>001000010=>11
100010001=>010000101=>9
100010010=>010000110=>10
100010011=>100001011=>7
100010100=>011000010=>11
100010101=>100001101=>8
100010110=>100001110=>9
100010111=>000110111=>5
100011000=>101000010=>12
100011001=>110000101=>9
100011010=>110000110=>10
100011011=>000111011=>6
100011100=>111000010=>11
100011101=>000111101=>7
100011110=>000111110=>8
100011111=>001011111=>3
100100000=>000100010=>12
100100001=>001000101=>10
100100010=>001000110=>11
100100011=>010001011=>8
100100100=>001100010=>12
100100101=>010001101=>9
100100110=>010001110=>10
100100111=>100010111=>6
100101000=>100100010=>13
100101001=>011000101=>10
100101010=>011000110=>11
100101011=>100011011=>7
100101100=>011100010=>12
100101101=>100011101=>8
100101110=>100011110=>9
100101111=>001101111=>4
100110000=>010100010=>14
100110001=>101000101=>11
100110010=>101000110=>12
100110011=>110001011=>8
100110100=>101100010=>13
100110101=>110001101=>9
100110110=>110001110=>10
100110111=>001110111=>5
100111000=>110100010=>14
100111001=>111000101=>10
100111010=>111000110=>11
100111011=>001111011=>6
100111100=>111100010=>12
100111101=>001111101=>7
100111110=>001111110=>8
100111111=>010111111=>2
101000000=>000010010=>13
101000001=>000100101=>11
101000010=>000100110=>12
101000011=>001001011=>9
101000100=>000110010=>13
101000101=>001001101=>10
101000110=>001001110=>11
101000111=>010010111=>7
101001000=>100010010=>14
101001001=>001100101=>11
101001010=>001100110=>12
101001011=>010011011=>8
101001100=>001110010=>13
101001101=>010011101=>9
101001110=>010011110=>10
101001111=>100101111=>5
101010000=>010010010=>15
101010001=>100100101=>12
101010010=>100100110=>13
101010011=>011001011=>9
101010100=>100110010=>14
101010101=>011001101=>10
101010110=>011001110=>11
101010111=>100110111=>6
101011000=>110010010=>15
101011001=>011100101=>11
101011010=>011100110=>12
101011011=>100111011=>7
101011100=>011110010=>13
101011101=>100111101=>8
101011110=>100111110=>9
101011111=>011011111=>3
101100000=>001010010=>16
101100001=>010100101=>13
101100010=>010100110=>14
101100011=>101001011=>10
101100100=>010110010=>15
101100101=>101001101=>11
101100110=>101001110=>12
101100111=>110010111=>7
101101000=>011010010=>16
101101001=>101100101=>12
101101010=>101100110=>13
101101011=>110011011=>8
101101100=>101110010=>14
101101101=>110011101=>9
101101110=>110011110=>10
101101111=>011101111=>4
101110000=>101010010=>17
101110001=>110100101=>13
101110010=>110100110=>14
101110011=>111001011=>9
101110100=>110110010=>15
101110101=>111001101=>10
101110110=>111001110=>11
101110111=>011110111=>5
101111000=>111010010=>16
101111001=>111100101=>11
101111010=>111100110=>12
101111011=>011111011=>6
101111100=>111110010=>13
101111101=>011111101=>7
101111110=>011111110=>8
101111111=>101111111=>1
110000000=>000001010=>14
110000001=>000010101=>12
110000010=>000010110=>13
110000011=>000101011=>10
110000100=>000011010=>14
110000101=>000101101=>11
110000110=>000101110=>12
110000111=>001010111=>8
110001000=>100001010=>15
110001001=>000110101=>12
110001010=>000110110=>13
110001011=>001011011=>9
110001100=>000111010=>14
110001101=>001011101=>10
110001110=>001011110=>11
110001111=>010101111=>6
110010000=>010001010=>16
110010001=>100010101=>13
110010010=>100010110=>14
110010011=>001101011=>10
110010100=>100011010=>15
110010101=>001101101=>11
110010110=>001101110=>12
110010111=>010110111=>7
110011000=>110001010=>16
110011001=>001110101=>12
110011010=>001110110=>13
110011011=>010111011=>8
110011100=>001111010=>14
110011101=>010111101=>9
110011110=>010111110=>10
110011111=>101011111=>4
110100000=>001001010=>17
110100001=>010010101=>14
110100010=>010010110=>15
110100011=>100101011=>11
110100100=>010011010=>16
110100101=>100101101=>12
110100110=>100101110=>13
110100111=>011010111=>8
110101000=>011001010=>17
110101001=>100110101=>13
110101010=>100110110=>14
110101011=>011011011=>9
110101100=>100111010=>15
110101101=>011011101=>10
110101110=>011011110=>11
110101111=>101101111=>5
110110000=>101001010=>18
110110001=>110010101=>14
110110010=>110010110=>15
110110011=>011101011=>10
110110100=>110011010=>16
110110101=>011101101=>11
110110110=>011101110=>12
110110111=>101110111=>6
110111000=>111001010=>17
110111001=>011110101=>12
110111010=>011110110=>13
110111011=>101111011=>7
110111100=>011111010=>14
110111101=>101111101=>8
110111110=>101111110=>9
110111111=>110111111=>2
111000000=>000101010=>18
111000001=>001010101=>15
111000010=>001010110=>16
111000011=>010101011=>12
111000100=>001011010=>17
111000101=>010101101=>13
111000110=>010101110=>14
111000111=>101010111=>9
111001000=>001101010=>18
111001001=>010110101=>14
111001010=>010110110=>15
111001011=>101011011=>10
111001100=>010111010=>16
111001101=>101011101=>11
111001110=>101011110=>12
111001111=>110101111=>6
111010000=>100101010=>19
111010001=>011010101=>15
111010010=>011010110=>16
111010011=>101101011=>11
111010100=>011011010=>17
111010101=>101101101=>12
111010110=>101101110=>13
111010111=>110110111=>7
111011000=>011101010=>18
111011001=>101110101=>13
111011010=>101110110=>14
111011011=>110111011=>8
111011100=>101111010=>15
111011101=>110111101=>9
111011110=>110111110=>10
111011111=>111011111=>3
111100000=>010101010=>20
111100001=>101010101=>16
111100010=>101010110=>17
111100011=>110101011=>12
111100100=>101011010=>18
111100101=>110101101=>13
111100110=>110101110=>14
111100111=>111010111=>8
111101000=>101101010=>19
111101001=>110110101=>14
111101010=>110110110=>15
111101011=>111011011=>9
111101100=>110111010=>16
111101101=>111011101=>10
111101110=>111011110=>11
111101111=>111101111=>4
111110000=>110101010=>20
111110001=>111010101=>15
111110010=>111010110=>16
111110011=>111101011=>10
111110100=>111011010=>17
111110101=>111101101=>11
111110110=>111101110=>12
111110111=>111110111=>5
111111000=>111101010=>18
111111001=>111110101=>12
111111010=>111110110=>13
111111011=>111111011=>6
111111100=>111111010=>14
111111101=>111111101=>7
111111110=>111111110=>8
111111111=>111111111=>0
1111111110=>1111111110=>9
1101111110=>1011111110=>10
1010111110=>1001111110=>10
1001011110=>1000111110=>10
1000111110=>0001111110=>9
1000101110=>1000011110=>10
1000011110=>0000111110=>9
1000010110=>1000001110=>10
1000001110=>0000011110=>9
1000001010=>1000000110=>10
1000000110=>0000001110=>9
1000000100=>1000000010=>10
1000000010=>0000000110=>9
1000000000=>0000000010=>9
10000000000=>00000000010=>10
11111111110=>11111111110=>10
0111111111=>0111111111=>0
0111100001=>1010101001=>16
0111000001=>0010101001=>15
0110000001=>0000101001=>12
0100000001=>0000001001=>7
0000000001=>0000000001=>0
01111111111=>01111111111=>0
0111010001=>0110101001=>15
01111000001=>01010101001=>20
0101000001=>0001001001=>11
0010000001=>0000010001=>6
00000000001=>00000000001=>0
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Description
The major index of a binary word.
This is the sum of the positions of descents, i.e., a one followed by a zero.
For words of length $n$ with $a$ zeros, the generating function for the major index is the $q$-binomial coefficient $\binom{n}{a}_q$.
This is the sum of the positions of descents, i.e., a one followed by a zero.
For words of length $n$ with $a$ zeros, the generating function for the major index is the $q$-binomial coefficient $\binom{n}{a}_q$.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00096Foata bijection.
See Mp00096Foata bijection.
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