Identifier
Images
=>
0=>1
1=>1
00=>01
01=>10
10=>11
11=>11
000=>001
001=>010
010=>101
011=>101
100=>101
101=>110
110=>111
111=>111
0000=>0001
0001=>0010
0010=>0101
0011=>0101
0100=>1001
0101=>1010
0110=>1011
0111=>1011
1000=>1001
1001=>1010
1010=>1101
1011=>1101
1100=>1101
1101=>1110
1110=>1111
1111=>1111
00000=>00001
00001=>00010
00010=>00101
00011=>00101
00100=>01001
00101=>01010
00110=>01011
00111=>01011
01000=>10001
01001=>10010
01010=>10101
01011=>10101
01100=>10101
01101=>10110
01110=>10111
01111=>10111
10000=>10001
10001=>10010
10010=>10101
10011=>10101
10100=>11001
10101=>11010
10110=>11011
10111=>11011
11000=>11001
11001=>11010
11010=>11101
11011=>11101
11100=>11101
11101=>11110
11110=>11111
11111=>11111
000000=>000001
000001=>000010
000010=>000101
000011=>000101
000100=>001001
000101=>001010
000110=>001011
000111=>001011
001000=>010001
001001=>010010
001010=>010101
001011=>010101
001100=>010101
001101=>010110
001110=>010111
001111=>010111
010000=>100001
010001=>100010
010010=>100101
010011=>100101
010100=>101001
010101=>101010
010110=>101011
010111=>101011
011000=>101001
011001=>101010
011010=>101101
011011=>101101
011100=>101101
011101=>101110
011110=>101111
011111=>101111
100000=>100001
100001=>100010
100010=>100101
100011=>100101
100100=>101001
100101=>101010
100110=>101011
100111=>101011
101000=>110001
101001=>110010
101010=>110101
101011=>110101
101100=>110101
101101=>110110
101110=>110111
101111=>110111
110000=>110001
110001=>110010
110010=>110101
110011=>110101
110100=>111001
110101=>111010
110110=>111011
110111=>111011
111000=>111001
111001=>111010
111010=>111101
111011=>111101
111100=>111101
111101=>111110
111110=>111111
111111=>111111
0000000=>0000001
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0000010=>0000101
0000011=>0000101
0000100=>0001001
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0000110=>0001011
0000111=>0001011
0001000=>0010001
0001001=>0010010
0001010=>0010101
0001011=>0010101
0001100=>0010101
0001101=>0010110
0001110=>0010111
0001111=>0010111
0010000=>0100001
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0010011=>0100101
0010100=>0101001
0010101=>0101010
0010110=>0101011
0010111=>0101011
0011000=>0101001
0011001=>0101010
0011010=>0101101
0011011=>0101101
0011100=>0101101
0011101=>0101110
0011110=>0101111
0011111=>0101111
0100000=>1000001
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0100011=>1000101
0100100=>1001001
0100101=>1001010
0100110=>1001011
0100111=>1001011
0101000=>1010001
0101001=>1010010
0101010=>1010101
0101011=>1010101
0101100=>1010101
0101101=>1010110
0101110=>1010111
0101111=>1010111
0110000=>1010001
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0110100=>1011001
0110101=>1011010
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0111000=>1011001
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0111011=>1011101
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0111111=>1011111
1000000=>1000001
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1000010=>1000101
1000011=>1000101
1000100=>1001001
1000101=>1001010
1000110=>1001011
1000111=>1001011
1001000=>1010001
1001001=>1010010
1001010=>1010101
1001011=>1010101
1001100=>1010101
1001101=>1010110
1001110=>1010111
1001111=>1010111
1010000=>1100001
1010001=>1100010
1010010=>1100101
1010011=>1100101
1010100=>1101001
1010101=>1101010
1010110=>1101011
1010111=>1101011
1011000=>1101001
1011001=>1101010
1011010=>1101101
1011011=>1101101
1011100=>1101101
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1011110=>1101111
1011111=>1101111
1100000=>1100001
1100001=>1100010
1100010=>1100101
1100011=>1100101
1100100=>1101001
1100101=>1101010
1100110=>1101011
1100111=>1101011
1101000=>1110001
1101001=>1110010
1101010=>1110101
1101011=>1110101
1101100=>1110101
1101101=>1110110
1101110=>1110111
1101111=>1110111
1110000=>1110001
1110001=>1110010
1110010=>1110101
1110011=>1110101
1110100=>1111001
1110101=>1111010
1110110=>1111011
1110111=>1111011
1111000=>1111001
1111001=>1111010
1111010=>1111101
1111011=>1111101
1111100=>1111101
1111101=>1111110
1111110=>1111111
1111111=>1111111
00000000=>00000001
00000001=>00000010
00000010=>00000101
00000011=>00000101
00000100=>00001001
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00000110=>00001011
00000111=>00001011
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00010011=>00100101
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00010111=>00101011
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00011110=>00101111
00011111=>00101111
00100000=>01000001
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00100111=>01001011
00101000=>01010001
00101001=>01010010
00101010=>01010101
00101011=>01010101
00101100=>01010101
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00101110=>01010111
00101111=>01010111
00110000=>01010001
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00110010=>01010101
00110011=>01010101
00110100=>01011001
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00110110=>01011011
00110111=>01011011
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00111100=>01011101
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01000000=>10000001
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01000010=>10000101
01000011=>10000101
01000100=>10001001
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01000110=>10001011
01000111=>10001011
01001000=>10010001
01001001=>10010010
01001010=>10010101
01001011=>10010101
01001100=>10010101
01001101=>10010110
01001110=>10010111
01001111=>10010111
01010000=>10100001
01010001=>10100010
01010010=>10100101
01010011=>10100101
01010100=>10101001
01010101=>10101010
01010110=>10101011
01010111=>10101011
01011000=>10101001
01011001=>10101010
01011010=>10101101
01011011=>10101101
01011100=>10101101
01011101=>10101110
01011110=>10101111
01011111=>10101111
01100000=>10100001
01100001=>10100010
01100010=>10100101
01100011=>10100101
01100100=>10101001
01100101=>10101010
01100110=>10101011
01100111=>10101011
01101000=>10110001
01101001=>10110010
01101010=>10110101
01101011=>10110101
01101100=>10110101
01101101=>10110110
01101110=>10110111
01101111=>10110111
01110000=>10110001
01110001=>10110010
01110010=>10110101
01110011=>10110101
01110100=>10111001
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01110110=>10111011
01110111=>10111011
01111000=>10111001
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01111010=>10111101
01111011=>10111101
01111100=>10111101
01111101=>10111110
01111110=>10111111
01111111=>10111111
10000000=>10000001
10000001=>10000010
10000010=>10000101
10000011=>10000101
10000100=>10001001
10000101=>10001010
10000110=>10001011
10000111=>10001011
10001000=>10010001
10001001=>10010010
10001010=>10010101
10001011=>10010101
10001100=>10010101
10001101=>10010110
10001110=>10010111
10001111=>10010111
10010000=>10100001
10010001=>10100010
10010010=>10100101
10010011=>10100101
10010100=>10101001
10010101=>10101010
10010110=>10101011
10010111=>10101011
10011000=>10101001
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10011010=>10101101
10011011=>10101101
10011100=>10101101
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10011110=>10101111
10011111=>10101111
10100000=>11000001
10100001=>11000010
10100010=>11000101
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10100100=>11001001
10100101=>11001010
10100110=>11001011
10100111=>11001011
10101000=>11010001
10101001=>11010010
10101010=>11010101
10101011=>11010101
10101100=>11010101
10101101=>11010110
10101110=>11010111
10101111=>11010111
10110000=>11010001
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10110011=>11010101
10110100=>11011001
10110101=>11011010
10110110=>11011011
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10111000=>11011001
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10111011=>11011101
10111100=>11011101
10111101=>11011110
10111110=>11011111
10111111=>11011111
11000000=>11000001
11000001=>11000010
11000010=>11000101
11000011=>11000101
11000100=>11001001
11000101=>11001010
11000110=>11001011
11000111=>11001011
11001000=>11010001
11001001=>11010010
11001010=>11010101
11001011=>11010101
11001100=>11010101
11001101=>11010110
11001110=>11010111
11001111=>11010111
11010000=>11100001
11010001=>11100010
11010010=>11100101
11010011=>11100101
11010100=>11101001
11010101=>11101010
11010110=>11101011
11010111=>11101011
11011000=>11101001
11011001=>11101010
11011010=>11101101
11011011=>11101101
11011100=>11101101
11011101=>11101110
11011110=>11101111
11011111=>11101111
11100000=>11100001
11100001=>11100010
11100010=>11100101
11100011=>11100101
11100100=>11101001
11100101=>11101010
11100110=>11101011
11100111=>11101011
11101000=>11110001
11101001=>11110010
11101010=>11110101
11101011=>11110101
11101100=>11110101
11101101=>11110110
11101110=>11110111
11101111=>11110111
11110000=>11110001
11110001=>11110010
11110010=>11110101
11110011=>11110101
11110100=>11111001
11110101=>11111010
11110110=>11111011
11110111=>11111011
11111000=>11111001
11111001=>11111010
11111010=>11111101
11111011=>11111101
11111100=>11111101
11111101=>11111110
11111110=>11111111
11111111=>11111111
000000000=>000000001
000000001=>000000010
000000010=>000000101
000000011=>000000101
000000100=>000001001
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000000111=>000001011
000001000=>000010001
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000001100=>000010101
000001101=>000010110
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000001111=>000010111
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111000000=>111000001
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111000011=>111000101
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111001110=>111010111
111001111=>111010111
111010000=>111100001
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11010101011000=>11101010101001
11010101100100=>11101010101001
11010101101000=>11101010110001
11010101110000=>11101010110001
11010110010100=>11101010101001
11010110011000=>11101010101001
11010110100100=>11101011001001
11010110101000=>11101011010001
11010110110000=>11101011010001
11010111000100=>11101011001001
11010111001000=>11101011010001
11010111010000=>11101011100001
11010111100000=>11101011100001
11011001010100=>11101010101001
11011001011000=>11101010101001
11011001100100=>11101010101001
11011001101000=>11101010110001
11011001110000=>11101010110001
11011010010100=>11101100101001
11011010011000=>11101100101001
11011010100100=>11101101001001
11011010101000=>11101101010001
11011010110000=>11101101010001
11011011000100=>11101101001001
11011011001000=>11101101010001
11011011010000=>11101101100001
11011011100000=>11101101100001
11011100010100=>11101100101001
11011100011000=>11101100101001
11011100100100=>11101101001001
11011100101000=>11101101010001
11011100110000=>11101101010001
11011101000100=>11101110001001
11011101001000=>11101110010001
11011101010000=>11101110100001
11011101100000=>11101110100001
11011110000010=>11101110000101
11011110000100=>11101110001001
11011110001000=>11101110010001
11011110010000=>11101110100001
11011110100000=>11101111000001
11011111000000=>11101111000001
11100101010100=>11101010101001
11100101011000=>11101010101001
11100101100100=>11101010101001
11100101101000=>11101010110001
11100101110000=>11101010110001
11100110010100=>11101010101001
11100110011000=>11101010101001
11100110100100=>11101011001001
11100110101000=>11101011010001
11100110110000=>11101011010001
11100111000100=>11101011001001
11100111001000=>11101011010001
11100111010000=>11101011100001
11100111100000=>11101011100001
11101001010100=>11110010101001
11101001011000=>11110010101001
11101001100100=>11110010101001
11101001101000=>11110010110001
11101001110000=>11110010110001
11101010010100=>11110100101001
11101010011000=>11110100101001
11101010100100=>11110101001001
11101010101000=>11110101010001
11101010110000=>11110101010001
11101011000100=>11110101001001
11101011001000=>11110101010001
11101011010000=>11110101100001
11101011100000=>11110101100001
11101100010100=>11110100101001
11101100011000=>11110100101001
11101100100100=>11110101001001
11101100101000=>11110101010001
11101100110000=>11110101010001
11101101000010=>11110110000101
11101101000100=>11110110001001
11101101001000=>11110110010001
11101101010000=>11110110100001
11101101100000=>11110110100001
11101110000010=>11110110000101
11101110000100=>11110110001001
11101110001000=>11110110010001
11101110010000=>11110110100001
11101110100000=>11110111000001
11101111000000=>11110111000001
11110001010100=>11110010101001
11110001011000=>11110010101001
11110001100100=>11110010101001
11110001101000=>11110010110001
11110001110000=>11110010110001
11110010010100=>11110100101001
11110010011000=>11110100101001
11110010100100=>11110101001001
11110010101000=>11110101010001
11110010110000=>11110101010001
11110011000010=>11110101000101
11110011000100=>11110101001001
11110011001000=>11110101010001
11110011010000=>11110101100001
11110011100000=>11110101100001
11110100010100=>11111000101001
11110100011000=>11111000101001
11110100100010=>11111001000101
11110100100100=>11111001001001
11110100101000=>11111001010001
11110100110000=>11111001010001
11110101000010=>11111010000101
11110101000100=>11111010001001
11110101001000=>11111010010001
11110101010000=>11111010100001
11110101100000=>11111010100001
11110110000010=>11111010000101
11110110000100=>11111010001001
11110110001000=>11111010010001
11110110010000=>11111010100001
11110110100000=>11111011000001
11110111000000=>11111011000001
11111000001100=>11111000010101
11111000010010=>11111000100101
11111000010100=>11111000101001
11111000011000=>11111000101001
11111000100010=>11111001000101
11111000100100=>11111001001001
11111000101000=>11111001010001
11111000110000=>11111001010001
11111001000010=>11111010000101
11111001000100=>11111010001001
11111001001000=>11111010010001
11111001010000=>11111010100001
11111001100000=>11111010100001
11111010000010=>11111100000101
11111010000100=>11111100001001
11111010001000=>11111100010001
11111010010000=>11111100100001
11111010100000=>11111101000001
11111011000000=>11111101000001
11111100000010=>11111100000101
11111100000100=>11111100001001
11111100001000=>11111100010001
11111100010000=>11111100100001
11111100100000=>11111101000001
11111101000000=>11111110000001
11111110000000=>11111110000001
1010101010101010=>1101010101010101
1010101010101100=>1101010101010101
1010101010110100=>1101010101011001
1010101010111000=>1101010101011001
1010101011010100=>1101010101101001
1010101011100100=>1101010101101001
1010101011101000=>1101010101110001
1010101011110000=>1101010101110001
1010101101010100=>1101010110101001
1010101110010100=>1101010110101001
1010101110100100=>1101010111001001
1010101111000100=>1101010111001001
1010110101010100=>1101011010101001
1010111001010100=>1101011010101001
1010111010010100=>1101011100101001
1010111100010100=>1101011100101001
1011010101010100=>1101101010101001
1011100101010100=>1101101010101001
1011101001010100=>1101110010101001
1011110001010100=>1101110010101001
1011110111000000=>1101111011000001
1011111010100000=>1101111101000001
1011111011000000=>1101111101000001
1011111100010000=>1101111100100001
1011111100100000=>1101111101000001
1011111101000000=>1101111110000001
1011111110000000=>1101111110000001
1101010101010100=>1110101010101001
1110010101010100=>1110101010101001
1110100101010100=>1111001010101001
1111000101010100=>1111001010101001
1111011100000010=>1111101100000101
1111101010000010=>1111110100000101
1111101100000010=>1111110100000101
1111110001000010=>1111110010000101
1111110010000010=>1111110100000101
1111110100000010=>1111111000000101
1111111000000010=>1111111000000101
101010101010101010=>110101010101010101
101010101010101100=>110101010101010101
101010101010110100=>110101010101011001
101010101011010100=>110101010101101001
101010101101010100=>110101010110101001
101010110101010100=>110101011010101001
101011010101010100=>110101101010101001
101101010101010100=>110110101010101001
110101010101010100=>111010101010101001
101010101010111000=>110101010101011001
101010101011100100=>110101010101101001
101010101110010100=>110101010110101001
101010111001010100=>110101011010101001
101011100101010100=>110101101010101001
101110010101010100=>110110101010101001
111001010101010100=>111010101010101001
111111110000000010=>111111110000000101
101111111100000000=>110111111100000001
111111101000000010=>111111110000000101
101111111010000000=>110111111100000001
111111100100000010=>111111101000000101
111111011000000010=>111111101000000101
101111111001000000=>110111111010000001
101111110110000000=>110111111010000001
10101010101010101010=>11010101010101010101
10101010101010101100=>11010101010101010101
10101010101010110100=>11010101010101011001
10101010101011010100=>11010101010101101001
10101010101101010100=>11010101010110101001
10101010110101010100=>11010101011010101001
10101011010101010100=>11010101101010101001
10101101010101010100=>11010110101010101001
10110101010101010100=>11011010101010101001
11010101010101010100=>11101010101010101001
11111111100000000010=>11111111100000000101
10111111111000000000=>11011111111000000001
11111111010000000010=>11111111100000000101
10111111110100000000=>11011111111000000001
1111111111000000000010=>1111111111000000000101
1011111111110000000000=>1101111111110000000001
click to show experimental identities
(only identities of compositions of up to three maps are shown)
Description
Return the binary word with every valley replaced by a peak.
A valley in a binary word is a subsequence $01$, or a trailing $0$. A peak is a subsequence $10$ or a trailing $1$. This map replaces every valley with a peak.
A valley in a binary word is a subsequence $01$, or a trailing $0$. A peak is a subsequence $10$ or a trailing $1$. This map replaces every valley with a peak.
References
[1] Tasoulas, I., Manes, K., Sapounakis, A., Tsikouras, P. Chains with small intervals in the lattice of binary paths MathSciNet:4054761
Properties
graded
Sage code
def mapping(w): w = list(w) f = list(w) for i in range(len(w)-1): if w[i:i+2] == [0, 1]: f[i:i+2] = [1, 0] if w[len(w)-1] == 0: f[len(w)-1] = 1 return Words([0,1])(f)
Weight
40
Created
May 19, 2021 at 17:35 by Martin Rubey
Updated
May 19, 2021 at 17:35 by Martin Rubey
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