Identifier
Images
=>
=>
0=>1
1=>0
00=>01
01=>10
10=>11
11=>00
000=>001
001=>010
010=>101
011=>100
100=>011
101=>110
110=>111
111=>000
0000=>0001
0001=>0010
0010=>0101
0011=>0100
0100=>1001
0101=>1010
0110=>1011
0111=>1000
1000=>0011
1001=>0110
1010=>1101
1011=>1100
1100=>0111
1101=>1110
1110=>1111
1111=>0000
00000=>00001
00001=>00010
00010=>00101
00011=>00100
00100=>01001
00101=>01010
00110=>01011
00111=>01000
01000=>10001
01001=>10010
01010=>10101
01011=>10100
01100=>10011
01101=>10110
01110=>10111
01111=>10000
10000=>00011
10001=>00110
10010=>01101
10011=>01100
10100=>11001
10101=>11010
10110=>11011
10111=>11000
11000=>00111
11001=>01110
11010=>11101
11011=>11100
11100=>01111
11101=>11110
11110=>11111
11111=>00000
000000=>000001
000001=>000010
000010=>000101
000011=>000100
000100=>001001
000101=>001010
000110=>001011
000111=>001000
001000=>010001
001001=>010010
001010=>010101
001011=>010100
001100=>010011
001101=>010110
001110=>010111
001111=>010000
010000=>100001
010001=>100010
010010=>100101
010011=>100100
010100=>101001
010101=>101010
010110=>101011
010111=>101000
011000=>100011
011001=>100110
011010=>101101
011011=>101100
011100=>100111
011101=>101110
011110=>101111
011111=>100000
100000=>000011
100001=>000110
100010=>001101
100011=>001100
100100=>011001
100101=>011010
100110=>011011
100111=>011000
101000=>110001
101001=>110010
101010=>110101
101011=>110100
101100=>110011
101101=>110110
101110=>110111
101111=>110000
110000=>000111
110001=>001110
110010=>011101
110011=>011100
110100=>111001
110101=>111010
110110=>111011
110111=>111000
111000=>001111
111001=>011110
111010=>111101
111011=>111100
111100=>011111
111101=>111110
111110=>111111
111111=>000000
0000000=>0000001
0000001=>0000010
0000010=>0000101
0000011=>0000100
0000100=>0001001
0000101=>0001010
0000110=>0001011
0000111=>0001000
0001000=>0010001
0001001=>0010010
0001010=>0010101
0001011=>0010100
0001100=>0010011
0001101=>0010110
0001110=>0010111
0001111=>0010000
0010000=>0100001
0010001=>0100010
0010010=>0100101
0010011=>0100100
0010100=>0101001
0010101=>0101010
0010110=>0101011
0010111=>0101000
0011000=>0100011
0011001=>0100110
0011010=>0101101
0011011=>0101100
0011100=>0100111
0011101=>0101110
0011110=>0101111
0011111=>0100000
0100000=>1000001
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0100010=>1000101
0100011=>1000100
0100100=>1001001
0100101=>1001010
0100110=>1001011
0100111=>1001000
0101000=>1010001
0101001=>1010010
0101010=>1010101
0101011=>1010100
0101100=>1010011
0101101=>1010110
0101110=>1010111
0101111=>1010000
0110000=>1000011
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0110010=>1001101
0110011=>1001100
0110100=>1011001
0110101=>1011010
0110110=>1011011
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0111000=>1000111
0111001=>1001110
0111010=>1011101
0111011=>1011100
0111100=>1001111
0111101=>1011110
0111110=>1011111
0111111=>1000000
1000000=>0000011
1000001=>0000110
1000010=>0001101
1000011=>0001100
1000100=>0011001
1000101=>0011010
1000110=>0011011
1000111=>0011000
1001000=>0110001
1001001=>0110010
1001010=>0110101
1001011=>0110100
1001100=>0110011
1001101=>0110110
1001110=>0110111
1001111=>0110000
1010000=>1100001
1010001=>1100010
1010010=>1100101
1010011=>1100100
1010100=>1101001
1010101=>1101010
1010110=>1101011
1010111=>1101000
1011000=>1100011
1011001=>1100110
1011010=>1101101
1011011=>1101100
1011100=>1100111
1011101=>1101110
1011110=>1101111
1011111=>1100000
1100000=>0000111
1100001=>0001110
1100010=>0011101
1100011=>0011100
1100100=>0111001
1100101=>0111010
1100110=>0111011
1100111=>0111000
1101000=>1110001
1101001=>1110010
1101010=>1110101
1101011=>1110100
1101100=>1110011
1101101=>1110110
1101110=>1110111
1101111=>1110000
1110000=>0001111
1110001=>0011110
1110010=>0111101
1110011=>0111100
1110100=>1111001
1110101=>1111010
1110110=>1111011
1110111=>1111000
1111000=>0011111
1111001=>0111110
1111010=>1111101
1111011=>1111100
1111100=>0111111
1111101=>1111110
1111110=>1111111
1111111=>0000000
00000000=>00000001
00000001=>00000010
00000010=>00000101
00000011=>00000100
00000100=>00001001
00000101=>00001010
00000110=>00001011
00000111=>00001000
00001000=>00010001
00001001=>00010010
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00001011=>00010100
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00001110=>00010111
00001111=>00010000
00010000=>00100001
00010001=>00100010
00010010=>00100101
00010011=>00100100
00010100=>00101001
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00010110=>00101011
00010111=>00101000
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00011001=>00100110
00011010=>00101101
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00011100=>00100111
00011101=>00101110
00011110=>00101111
00011111=>00100000
00100000=>01000001
00100001=>01000010
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00100011=>01000100
00100100=>01001001
00100101=>01001010
00100110=>01001011
00100111=>01001000
00101000=>01010001
00101001=>01010010
00101010=>01010101
00101011=>01010100
00101100=>01010011
00101101=>01010110
00101110=>01010111
00101111=>01010000
00110000=>01000011
00110001=>01000110
00110010=>01001101
00110011=>01001100
00110100=>01011001
00110101=>01011010
00110110=>01011011
00110111=>01011000
00111000=>01000111
00111001=>01001110
00111010=>01011101
00111011=>01011100
00111100=>01001111
00111101=>01011110
00111110=>01011111
00111111=>01000000
01000000=>10000001
01000001=>10000010
01000010=>10000101
01000011=>10000100
01000100=>10001001
01000101=>10001010
01000110=>10001011
01000111=>10001000
01001000=>10010001
01001001=>10010010
01001010=>10010101
01001011=>10010100
01001100=>10010011
01001101=>10010110
01001110=>10010111
01001111=>10010000
01010000=>10100001
01010001=>10100010
01010010=>10100101
01010011=>10100100
01010100=>10101001
01010101=>10101010
01010110=>10101011
01010111=>10101000
01011000=>10100011
01011001=>10100110
01011010=>10101101
01011011=>10101100
01011100=>10100111
01011101=>10101110
01011110=>10101111
01011111=>10100000
01100000=>10000011
01100001=>10000110
01100010=>10001101
01100011=>10001100
01100100=>10011001
01100101=>10011010
01100110=>10011011
01100111=>10011000
01101000=>10110001
01101001=>10110010
01101010=>10110101
01101011=>10110100
01101100=>10110011
01101101=>10110110
01101110=>10110111
01101111=>10110000
01110000=>10000111
01110001=>10001110
01110010=>10011101
01110011=>10011100
01110100=>10111001
01110101=>10111010
01110110=>10111011
01110111=>10111000
01111000=>10001111
01111001=>10011110
01111010=>10111101
01111011=>10111100
01111100=>10011111
01111101=>10111110
01111110=>10111111
01111111=>10000000
10000000=>00000011
10000001=>00000110
10000010=>00001101
10000011=>00001100
10000100=>00011001
10000101=>00011010
10000110=>00011011
10000111=>00011000
10001000=>00110001
10001001=>00110010
10001010=>00110101
10001011=>00110100
10001100=>00110011
10001101=>00110110
10001110=>00110111
10001111=>00110000
10010000=>01100001
10010001=>01100010
10010010=>01100101
10010011=>01100100
10010100=>01101001
10010101=>01101010
10010110=>01101011
10010111=>01101000
10011000=>01100011
10011001=>01100110
10011010=>01101101
10011011=>01101100
10011100=>01100111
10011101=>01101110
10011110=>01101111
10011111=>01100000
10100000=>11000001
10100001=>11000010
10100010=>11000101
10100011=>11000100
10100100=>11001001
10100101=>11001010
10100110=>11001011
10100111=>11001000
10101000=>11010001
10101001=>11010010
10101010=>11010101
10101011=>11010100
10101100=>11010011
10101101=>11010110
10101110=>11010111
10101111=>11010000
10110000=>11000011
10110001=>11000110
10110010=>11001101
10110011=>11001100
10110100=>11011001
10110101=>11011010
10110110=>11011011
10110111=>11011000
10111000=>11000111
10111001=>11001110
10111010=>11011101
10111011=>11011100
10111100=>11001111
10111101=>11011110
10111110=>11011111
10111111=>11000000
11000000=>00000111
11000001=>00001110
11000010=>00011101
11000011=>00011100
11000100=>00111001
11000101=>00111010
11000110=>00111011
11000111=>00111000
11001000=>01110001
11001001=>01110010
11001010=>01110101
11001011=>01110100
11001100=>01110011
11001101=>01110110
11001110=>01110111
11001111=>01110000
11010000=>11100001
11010001=>11100010
11010010=>11100101
11010011=>11100100
11010100=>11101001
11010101=>11101010
11010110=>11101011
11010111=>11101000
11011000=>11100011
11011001=>11100110
11011010=>11101101
11011011=>11101100
11011100=>11100111
11011101=>11101110
11011110=>11101111
11011111=>11100000
11100000=>00001111
11100001=>00011110
11100010=>00111101
11100011=>00111100
11100100=>01111001
11100101=>01111010
11100110=>01111011
11100111=>01111000
11101000=>11110001
11101001=>11110010
11101010=>11110101
11101011=>11110100
11101100=>11110011
11101101=>11110110
11101110=>11110111
11101111=>11110000
11110000=>00011111
11110001=>00111110
11110010=>01111101
11110011=>01111100
11110100=>11111001
11110101=>11111010
11110110=>11111011
11110111=>11111000
11111000=>00111111
11111001=>01111110
11111010=>11111101
11111011=>11111100
11111100=>01111111
11111101=>11111110
11111110=>11111111
11111111=>00000000
000000000=>000000001
000000001=>000000010
000000010=>000000101
000000011=>000000100
000000100=>000001001
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000000110=>000001011
000000111=>000001000
000001000=>000010001
000001001=>000010010
000001010=>000010101
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000001100=>000010011
000001101=>000010110
000001110=>000010111
000001111=>000010000
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000100000=>001000001
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110110011=>111001100
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110111001=>111001110
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110111100=>111001111
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110111110=>111011111
110111111=>111000000
111000000=>000001111
111000001=>000011110
111000010=>000111101
111000011=>000111100
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111000110=>001111011
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111001001=>011110010
111001010=>011110101
111001011=>011110100
111001100=>011110011
111001101=>011110110
111001110=>011110111
111001111=>011110000
111010000=>111100001
111010001=>111100010
111010010=>111100101
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11010110010100=>11101001101001
11010110011000=>11101001100011
11010110100100=>11101011001001
11010110101000=>11101011010001
11010110110000=>11101011000011
11010111000100=>11101000111001
11010111001000=>11101001110001
11010111010000=>11101011100001
11010111100000=>11101000001111
11011001010100=>11100110101001
11011001011000=>11100110100011
11011001100100=>11100110011001
11011001101000=>11100110110001
11011001110000=>11100110000111
11011010010100=>11101100101001
11011010011000=>11101100100011
11011010100100=>11101101001001
11011010101000=>11101101010001
11011010110000=>11101101000011
11011011000100=>11101100011001
11011011001000=>11101100110001
11011011010000=>11101101100001
11011011100000=>11101100000111
11011100010100=>11100011101001
11011100011000=>11100011100011
11011100100100=>11100111001001
11011100101000=>11100111010001
11011100110000=>11100111000011
11011101000100=>11101110001001
11011101001000=>11101110010001
11011101010000=>11101110100001
11011101100000=>11101110000011
11011110000010=>11100000111101
11011110000100=>11100001111001
11011110001000=>11100011110001
11011110010000=>11100111100001
11011110100000=>11101111000001
11011111000000=>11100000011111
11100101010100=>01111010101001
11100101011000=>01111010100011
11100101100100=>01111010011001
11100101101000=>01111010110001
11100101110000=>01111010000111
11100110010100=>01111001101001
11100110011000=>01111001100011
11100110100100=>01111011001001
11100110101000=>01111011010001
11100110110000=>01111011000011
11100111000100=>01111000111001
11100111001000=>01111001110001
11100111010000=>01111011100001
11100111100000=>01111000001111
11101001010100=>11110010101001
11101001011000=>11110010100011
11101001100100=>11110010011001
11101001101000=>11110010110001
11101001110000=>11110010000111
11101010010100=>11110100101001
11101010011000=>11110100100011
11101010100100=>11110101001001
11101010101000=>11110101010001
11101010110000=>11110101000011
11101011000100=>11110100011001
11101011001000=>11110100110001
11101011010000=>11110101100001
11101011100000=>11110100000111
11101100010100=>11110001101001
11101100011000=>11110001100011
11101100100100=>11110011001001
11101100101000=>11110011010001
11101100110000=>11110011000011
11101101000010=>11110110000101
11101101000100=>11110110001001
11101101001000=>11110110010001
11101101010000=>11110110100001
11101101100000=>11110110000011
11101110000010=>11110000011101
11101110000100=>11110000111001
11101110001000=>11110001110001
11101110010000=>11110011100001
11101110100000=>11110111000001
11101111000000=>11110000001111
11110001010100=>00111110101001
11110001011000=>00111110100011
11110001100100=>00111110011001
11110001101000=>00111110110001
11110001110000=>00111110000111
11110010010100=>01111100101001
11110010011000=>01111100100011
11110010100100=>01111101001001
11110010101000=>01111101010001
11110010110000=>01111101000011
11110011000010=>01111100001101
11110011000100=>01111100011001
11110011001000=>01111100110001
11110011010000=>01111101100001
11110011100000=>01111100000111
11110100010100=>11111000101001
11110100011000=>11111000100011
11110100100010=>11111001000101
11110100100100=>11111001001001
11110100101000=>11111001010001
11110100110000=>11111001000011
11110101000010=>11111010000101
11110101000100=>11111010001001
11110101001000=>11111010010001
11110101010000=>11111010100001
11110101100000=>11111010000011
11110110000010=>11111000001101
11110110000100=>11111000011001
11110110001000=>11111000110001
11110110010000=>11111001100001
11110110100000=>11111011000001
11110111000000=>11111000000111
11111000001100=>00001111110011
11111000010010=>00011111100101
11111000010100=>00011111101001
11111000011000=>00011111100011
11111000100010=>00111111000101
11111000100100=>00111111001001
11111000101000=>00111111010001
11111000110000=>00111111000011
11111001000010=>01111110000101
11111001000100=>01111110001001
11111001001000=>01111110010001
11111001010000=>01111110100001
11111001100000=>01111110000011
11111010000010=>11111100000101
11111010000100=>11111100001001
11111010001000=>11111100010001
11111010010000=>11111100100001
11111010100000=>11111101000001
11111011000000=>11111100000011
11111100000010=>00000111111101
11111100000100=>00001111111001
11111100001000=>00011111110001
11111100010000=>00111111100001
11111100100000=>01111111000001
11111101000000=>11111110000001
11111110000000=>00000011111111
1010101010101010=>1101010101010101
1010101010101100=>1101010101010011
1010101010110100=>1101010101011001
1010101010111000=>1101010101000111
1010101011010100=>1101010101101001
1010101011100100=>1101010100111001
1010101011101000=>1101010101110001
1010101011110000=>1101010100001111
1010101101010100=>1101010110101001
1010101110010100=>1101010011101001
1010101110100100=>1101010111001001
1010101111000100=>1101010001111001
1010110101010100=>1101011010101001
1010111001010100=>1101001110101001
1010111010010100=>1101011100101001
1010111100010100=>1101000111101001
1011010101010100=>1101101010101001
1011100101010100=>1100111010101001
1011101001010100=>1101110010101001
1011110001010100=>1100011110101001
1011110111000000=>1101111000000111
1011111010100000=>1101111101000001
1011111011000000=>1101111100000011
1011111100010000=>1100011111100001
1011111100100000=>1100111111000001
1011111101000000=>1101111110000001
1011111110000000=>1100000001111111
1101010101010100=>1110101010101001
1110010101010100=>0111101010101001
1110100101010100=>1111001010101001
1111000101010100=>0011111010101001
1111011100000010=>1111100000011101
1111101010000010=>1111110100000101
1111101100000010=>1111110000001101
1111110001000010=>0011111110000101
1111110010000010=>0111111100000101
1111110100000010=>1111111000000101
1111111000000010=>0000001111111101
101010101010101010=>110101010101010101
101010101010101100=>110101010101010011
101010101010110100=>110101010101011001
101010101011010100=>110101010101101001
101010101101010100=>110101010110101001
101010110101010100=>110101011010101001
101011010101010100=>110101101010101001
101101010101010100=>110110101010101001
110101010101010100=>111010101010101001
101010101010111000=>110101010101000111
101010101011100100=>110101010100111001
101010101110010100=>110101010011101001
101010111001010100=>110101001110101001
101011100101010100=>110100111010101001
101110010101010100=>110011101010101001
111001010101010100=>011110101010101001
111111110000000010=>000000011111111101
101111111100000000=>110000000011111111
111111101000000010=>111111110000000101
101111111010000000=>110111111100000001
111111100100000010=>011111111000000101
111111011000000010=>111111100000001101
101111111001000000=>110011111110000001
101111110110000000=>110111111000000011
10101010101010101010=>11010101010101010101
10101010101010101100=>11010101010101010011
10101010101010110100=>11010101010101011001
10101010101011010100=>11010101010101101001
10101010101101010100=>11010101010110101001
10101010110101010100=>11010101011010101001
10101011010101010100=>11010101101010101001
10101101010101010100=>11010110101010101001
10110101010101010100=>11011010101010101001
11010101010101010100=>11101010101010101001
11111111100000000010=>00000000111111111101
10111111111000000000=>11000000000111111111
11111111010000000010=>11111111100000000101
10111111110100000000=>11011111111000000001
1111111111000000000010=>0000000001111111111101
1011111111110000000000=>1100000000001111111111
click to show experimental identities
(only identities of compositions of up to three maps are shown)
Description
Return the rowmotion of the binary word, regarded as a lattice path.
Consider the binary word of length $n$ as a lattice path with $n$ steps, where a 1 corresponds to an up step and a 0 corresponds to a down step.
This map returns the path whose peaks are the valleys of the original path with an up step appended.
Consider the binary word of length $n$ as a lattice path with $n$ steps, where a 1 corresponds to an up step and a 0 corresponds to a down step.
This map returns the path whose peaks are the valleys of the original path with an up step appended.
Properties
bijective, graded
Sage code
def mapping(w): n = len(w) w1 = [] a = 0 i = 0 while i < n: if w[i]: a += 1 i += 1 elif i+1 == n: w1.extend([1]*(a+1)) i += 2 a = 0 elif w[i+1]: w1.extend([1]*(a+1) + [0]) i += 2 a = 0 else: w1.append(0) i += 1 w1.extend([0]*a) return Word(w1)
Weight
40
Created
Jan 16, 2023 at 17:43 by Martin Rubey
Updated
Jan 16, 2023 at 17:43 by Martin Rubey
searching the database
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