Identifier
Images
=>
=>
0=>0
1=>1
00=>00
01=>10
10=>01
11=>11
000=>000
001=>010
010=>100
011=>101
100=>001
101=>110
110=>011
111=>111
0000=>0000
0001=>0010
0010=>0100
0011=>0101
0100=>1000
0101=>1010
0110=>1001
0111=>1011
1000=>0001
1001=>0110
1010=>1100
1011=>1101
1100=>0011
1101=>1110
1110=>0111
1111=>1111
00000=>00000
00001=>00010
00010=>00100
00011=>00101
00100=>01000
00101=>01010
00110=>01001
00111=>01011
01000=>10000
01001=>10010
01010=>10100
01011=>10101
01100=>10001
01101=>10110
01110=>10011
01111=>10111
10000=>00001
10001=>00110
10010=>01100
10011=>01101
10100=>11000
10101=>11010
10110=>11001
10111=>11011
11000=>00011
11001=>01110
11010=>11100
11011=>11101
11100=>00111
11101=>11110
11110=>01111
11111=>11111
000000=>000000
000001=>000010
000010=>000100
000011=>000101
000100=>001000
000101=>001010
000110=>001001
000111=>001011
001000=>010000
001001=>010010
001010=>010100
001011=>010101
001100=>010001
001101=>010110
001110=>010011
001111=>010111
010000=>100000
010001=>100010
010010=>100100
010011=>100101
010100=>101000
010101=>101010
010110=>101001
010111=>101011
011000=>100001
011001=>100110
011010=>101100
011011=>101101
011100=>100011
011101=>101110
011110=>100111
011111=>101111
100000=>000001
100001=>000110
100010=>001100
100011=>001101
100100=>011000
100101=>011010
100110=>011001
100111=>011011
101000=>110000
101001=>110010
101010=>110100
101011=>110101
101100=>110001
101101=>110110
101110=>110011
101111=>110111
110000=>000011
110001=>001110
110010=>011100
110011=>011101
110100=>111000
110101=>111010
110110=>111001
110111=>111011
111000=>000111
111001=>011110
111010=>111100
111011=>111101
111100=>001111
111101=>111110
111110=>011111
111111=>111111
0000000=>0000000
0000001=>0000010
0000010=>0000100
0000011=>0000101
0000100=>0001000
0000101=>0001010
0000110=>0001001
0000111=>0001011
0001000=>0010000
0001001=>0010010
0001010=>0010100
0001011=>0010101
0001100=>0010001
0001101=>0010110
0001110=>0010011
0001111=>0010111
0010000=>0100000
0010001=>0100010
0010010=>0100100
0010011=>0100101
0010100=>0101000
0010101=>0101010
0010110=>0101001
0010111=>0101011
0011000=>0100001
0011001=>0100110
0011010=>0101100
0011011=>0101101
0011100=>0100011
0011101=>0101110
0011110=>0100111
0011111=>0101111
0100000=>1000000
0100001=>1000010
0100010=>1000100
0100011=>1000101
0100100=>1001000
0100101=>1001010
0100110=>1001001
0100111=>1001011
0101000=>1010000
0101001=>1010010
0101010=>1010100
0101011=>1010101
0101100=>1010001
0101101=>1010110
0101110=>1010011
0101111=>1010111
0110000=>1000001
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0110010=>1001100
0110011=>1001101
0110100=>1011000
0110101=>1011010
0110110=>1011001
0110111=>1011011
0111000=>1000011
0111001=>1001110
0111010=>1011100
0111011=>1011101
0111100=>1000111
0111101=>1011110
0111110=>1001111
0111111=>1011111
1000000=>0000001
1000001=>0000110
1000010=>0001100
1000011=>0001101
1000100=>0011000
1000101=>0011010
1000110=>0011001
1000111=>0011011
1001000=>0110000
1001001=>0110010
1001010=>0110100
1001011=>0110101
1001100=>0110001
1001101=>0110110
1001110=>0110011
1001111=>0110111
1010000=>1100000
1010001=>1100010
1010010=>1100100
1010011=>1100101
1010100=>1101000
1010101=>1101010
1010110=>1101001
1010111=>1101011
1011000=>1100001
1011001=>1100110
1011010=>1101100
1011011=>1101101
1011100=>1100011
1011101=>1101110
1011110=>1100111
1011111=>1101111
1100000=>0000011
1100001=>0001110
1100010=>0011100
1100011=>0011101
1100100=>0111000
1100101=>0111010
1100110=>0111001
1100111=>0111011
1101000=>1110000
1101001=>1110010
1101010=>1110100
1101011=>1110101
1101100=>1110001
1101101=>1110110
1101110=>1110011
1101111=>1110111
1110000=>0000111
1110001=>0011110
1110010=>0111100
1110011=>0111101
1110100=>1111000
1110101=>1111010
1110110=>1111001
1110111=>1111011
1111000=>0001111
1111001=>0111110
1111010=>1111100
1111011=>1111101
1111100=>0011111
1111101=>1111110
1111110=>0111111
1111111=>1111111
00000000=>00000000
00000001=>00000010
00000010=>00000100
00000011=>00000101
00000100=>00001000
00000101=>00001010
00000110=>00001001
00000111=>00001011
00001000=>00010000
00001001=>00010010
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00001011=>00010101
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00001110=>00010011
00001111=>00010111
00010000=>00100000
00010001=>00100010
00010010=>00100100
00010011=>00100101
00010100=>00101000
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00010110=>00101001
00010111=>00101011
00011000=>00100001
00011001=>00100110
00011010=>00101100
00011011=>00101101
00011100=>00100011
00011101=>00101110
00011110=>00100111
00011111=>00101111
00100000=>01000000
00100001=>01000010
00100010=>01000100
00100011=>01000101
00100100=>01001000
00100101=>01001010
00100110=>01001001
00100111=>01001011
00101000=>01010000
00101001=>01010010
00101010=>01010100
00101011=>01010101
00101100=>01010001
00101101=>01010110
00101110=>01010011
00101111=>01010111
00110000=>01000001
00110001=>01000110
00110010=>01001100
00110011=>01001101
00110100=>01011000
00110101=>01011010
00110110=>01011001
00110111=>01011011
00111000=>01000011
00111001=>01001110
00111010=>01011100
00111011=>01011101
00111100=>01000111
00111101=>01011110
00111110=>01001111
00111111=>01011111
01000000=>10000000
01000001=>10000010
01000010=>10000100
01000011=>10000101
01000100=>10001000
01000101=>10001010
01000110=>10001001
01000111=>10001011
01001000=>10010000
01001001=>10010010
01001010=>10010100
01001011=>10010101
01001100=>10010001
01001101=>10010110
01001110=>10010011
01001111=>10010111
01010000=>10100000
01010001=>10100010
01010010=>10100100
01010011=>10100101
01010100=>10101000
01010101=>10101010
01010110=>10101001
01010111=>10101011
01011000=>10100001
01011001=>10100110
01011010=>10101100
01011011=>10101101
01011100=>10100011
01011101=>10101110
01011110=>10100111
01011111=>10101111
01100000=>10000001
01100001=>10000110
01100010=>10001100
01100011=>10001101
01100100=>10011000
01100101=>10011010
01100110=>10011001
01100111=>10011011
01101000=>10110000
01101001=>10110010
01101010=>10110100
01101011=>10110101
01101100=>10110001
01101101=>10110110
01101110=>10110011
01101111=>10110111
01110000=>10000011
01110001=>10001110
01110010=>10011100
01110011=>10011101
01110100=>10111000
01110101=>10111010
01110110=>10111001
01110111=>10111011
01111000=>10000111
01111001=>10011110
01111010=>10111100
01111011=>10111101
01111100=>10001111
01111101=>10111110
01111110=>10011111
01111111=>10111111
10000000=>00000001
10000001=>00000110
10000010=>00001100
10000011=>00001101
10000100=>00011000
10000101=>00011010
10000110=>00011001
10000111=>00011011
10001000=>00110000
10001001=>00110010
10001010=>00110100
10001011=>00110101
10001100=>00110001
10001101=>00110110
10001110=>00110011
10001111=>00110111
10010000=>01100000
10010001=>01100010
10010010=>01100100
10010011=>01100101
10010100=>01101000
10010101=>01101010
10010110=>01101001
10010111=>01101011
10011000=>01100001
10011001=>01100110
10011010=>01101100
10011011=>01101101
10011100=>01100011
10011101=>01101110
10011110=>01100111
10011111=>01101111
10100000=>11000000
10100001=>11000010
10100010=>11000100
10100011=>11000101
10100100=>11001000
10100101=>11001010
10100110=>11001001
10100111=>11001011
10101000=>11010000
10101001=>11010010
10101010=>11010100
10101011=>11010101
10101100=>11010001
10101101=>11010110
10101110=>11010011
10101111=>11010111
10110000=>11000001
10110001=>11000110
10110010=>11001100
10110011=>11001101
10110100=>11011000
10110101=>11011010
10110110=>11011001
10110111=>11011011
10111000=>11000011
10111001=>11001110
10111010=>11011100
10111011=>11011101
10111100=>11000111
10111101=>11011110
10111110=>11001111
10111111=>11011111
11000000=>00000011
11000001=>00001110
11000010=>00011100
11000011=>00011101
11000100=>00111000
11000101=>00111010
11000110=>00111001
11000111=>00111011
11001000=>01110000
11001001=>01110010
11001010=>01110100
11001011=>01110101
11001100=>01110001
11001101=>01110110
11001110=>01110011
11001111=>01110111
11010000=>11100000
11010001=>11100010
11010010=>11100100
11010011=>11100101
11010100=>11101000
11010101=>11101010
11010110=>11101001
11010111=>11101011
11011000=>11100001
11011001=>11100110
11011010=>11101100
11011011=>11101101
11011100=>11100011
11011101=>11101110
11011110=>11100111
11011111=>11101111
11100000=>00000111
11100001=>00011110
11100010=>00111100
11100011=>00111101
11100100=>01111000
11100101=>01111010
11100110=>01111001
11100111=>01111011
11101000=>11110000
11101001=>11110010
11101010=>11110100
11101011=>11110101
11101100=>11110001
11101101=>11110110
11101110=>11110011
11101111=>11110111
11110000=>00001111
11110001=>00111110
11110010=>01111100
11110011=>01111101
11110100=>11111000
11110101=>11111010
11110110=>11111001
11110111=>11111011
11111000=>00011111
11111001=>01111110
11111010=>11111100
11111011=>11111101
11111100=>00111111
11111101=>11111110
11111110=>01111111
11111111=>11111111
000000000=>000000000
000000001=>000000010
000000010=>000000100
000000011=>000000101
000000100=>000001000
000000101=>000001010
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000000111=>000001011
000001000=>000010000
000001001=>000010010
000001010=>000010100
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000001100=>000010001
000001101=>000010110
000001110=>000010011
000001111=>000010111
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000100000=>001000000
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000111110=>001001111
000111111=>001011111
001000000=>010000000
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001000010=>010000100
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001001000=>010010000
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110001000=>001110000
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110100010=>111000100
110100011=>111000101
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110100101=>111001010
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110110011=>111001101
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110110110=>111011001
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110111100=>111000111
110111101=>111011110
110111110=>111001111
110111111=>111011111
111000000=>000000111
111000001=>000011110
111000010=>000111100
111000011=>000111101
111000100=>001111000
111000101=>001111010
111000110=>001111001
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111001000=>011110000
111001001=>011110010
111001010=>011110100
111001011=>011110101
111001100=>011110001
111001101=>011110110
111001110=>011110011
111001111=>011110111
111010000=>111100000
111010001=>111100010
111010010=>111100100
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11010110110000=>11101011000001
11010111000100=>11101000111000
11010111001000=>11101001110000
11010111010000=>11101011100000
11010111100000=>11101000000111
11011001010100=>11100110101000
11011001011000=>11100110100001
11011001100100=>11100110011000
11011001101000=>11100110110000
11011001110000=>11100110000011
11011010010100=>11101100101000
11011010011000=>11101100100001
11011010100100=>11101101001000
11011010101000=>11101101010000
11011010110000=>11101101000001
11011011000100=>11101100011000
11011011001000=>11101100110000
11011011010000=>11101101100000
11011011100000=>11101100000011
11011100010100=>11100011101000
11011100011000=>11100011100001
11011100100100=>11100111001000
11011100101000=>11100111010000
11011100110000=>11100111000001
11011101000100=>11101110001000
11011101001000=>11101110010000
11011101010000=>11101110100000
11011101100000=>11101110000001
11011110000010=>11100000111100
11011110000100=>11100001111000
11011110001000=>11100011110000
11011110010000=>11100111100000
11011110100000=>11101111000000
11011111000000=>11100000001111
11100101010100=>01111010101000
11100101011000=>01111010100001
11100101100100=>01111010011000
11100101101000=>01111010110000
11100101110000=>01111010000011
11100110010100=>01111001101000
11100110011000=>01111001100001
11100110100100=>01111011001000
11100110101000=>01111011010000
11100110110000=>01111011000001
11100111000100=>01111000111000
11100111001000=>01111001110000
11100111010000=>01111011100000
11100111100000=>01111000000111
11101001010100=>11110010101000
11101001011000=>11110010100001
11101001100100=>11110010011000
11101001101000=>11110010110000
11101001110000=>11110010000011
11101010010100=>11110100101000
11101010011000=>11110100100001
11101010100100=>11110101001000
11101010101000=>11110101010000
11101010110000=>11110101000001
11101011000100=>11110100011000
11101011001000=>11110100110000
11101011010000=>11110101100000
11101011100000=>11110100000011
11101100010100=>11110001101000
11101100011000=>11110001100001
11101100100100=>11110011001000
11101100101000=>11110011010000
11101100110000=>11110011000001
11101101000010=>11110110000100
11101101000100=>11110110001000
11101101001000=>11110110010000
11101101010000=>11110110100000
11101101100000=>11110110000001
11101110000010=>11110000011100
11101110000100=>11110000111000
11101110001000=>11110001110000
11101110010000=>11110011100000
11101110100000=>11110111000000
11101111000000=>11110000000111
11110001010100=>00111110101000
11110001011000=>00111110100001
11110001100100=>00111110011000
11110001101000=>00111110110000
11110001110000=>00111110000011
11110010010100=>01111100101000
11110010011000=>01111100100001
11110010100100=>01111101001000
11110010101000=>01111101010000
11110010110000=>01111101000001
11110011000010=>01111100001100
11110011000100=>01111100011000
11110011001000=>01111100110000
11110011010000=>01111101100000
11110011100000=>01111100000011
11110100010100=>11111000101000
11110100011000=>11111000100001
11110100100010=>11111001000100
11110100100100=>11111001001000
11110100101000=>11111001010000
11110100110000=>11111001000001
11110101000010=>11111010000100
11110101000100=>11111010001000
11110101001000=>11111010010000
11110101010000=>11111010100000
11110101100000=>11111010000001
11110110000010=>11111000001100
11110110000100=>11111000011000
11110110001000=>11111000110000
11110110010000=>11111001100000
11110110100000=>11111011000000
11110111000000=>11111000000011
11111000001100=>00001111110001
11111000010010=>00011111100100
11111000010100=>00011111101000
11111000011000=>00011111100001
11111000100010=>00111111000100
11111000100100=>00111111001000
11111000101000=>00111111010000
11111000110000=>00111111000001
11111001000010=>01111110000100
11111001000100=>01111110001000
11111001001000=>01111110010000
11111001010000=>01111110100000
11111001100000=>01111110000001
11111010000010=>11111100000100
11111010000100=>11111100001000
11111010001000=>11111100010000
11111010010000=>11111100100000
11111010100000=>11111101000000
11111011000000=>11111100000001
11111100000010=>00000111111100
11111100000100=>00001111111000
11111100001000=>00011111110000
11111100010000=>00111111100000
11111100100000=>01111111000000
11111101000000=>11111110000000
11111110000000=>00000001111111
1010101010101010=>1101010101010100
1010101010101100=>1101010101010001
1010101010110100=>1101010101011000
1010101010111000=>1101010101000011
1010101011010100=>1101010101101000
1010101011100100=>1101010100111000
1010101011101000=>1101010101110000
1010101011110000=>1101010100000111
1010101101010100=>1101010110101000
1010101110010100=>1101010011101000
1010101110100100=>1101010111001000
1010101111000100=>1101010001111000
1010110101010100=>1101011010101000
1010111001010100=>1101001110101000
1010111010010100=>1101011100101000
1010111100010100=>1101000111101000
1011010101010100=>1101101010101000
1011100101010100=>1100111010101000
1011101001010100=>1101110010101000
1011110001010100=>1100011110101000
1011110111000000=>1101111000000011
1011111010100000=>1101111101000000
1011111011000000=>1101111100000001
1011111100010000=>1100011111100000
1011111100100000=>1100111111000000
1011111101000000=>1101111110000000
1011111110000000=>1100000000111111
1101010101010100=>1110101010101000
1110010101010100=>0111101010101000
1110100101010100=>1111001010101000
1111000101010100=>0011111010101000
1111011100000010=>1111100000011100
1111101010000010=>1111110100000100
1111101100000010=>1111110000001100
1111110001000010=>0011111110000100
1111110010000010=>0111111100000100
1111110100000010=>1111111000000100
1111111000000010=>0000001111111100
101010101010101010=>110101010101010100
101010101010101100=>110101010101010001
101010101010110100=>110101010101011000
101010101011010100=>110101010101101000
101010101101010100=>110101010110101000
101010110101010100=>110101011010101000
101011010101010100=>110101101010101000
101101010101010100=>110110101010101000
110101010101010100=>111010101010101000
101010101010111000=>110101010101000011
101010101011100100=>110101010100111000
101010101110010100=>110101010011101000
101010111001010100=>110101001110101000
101011100101010100=>110100111010101000
101110010101010100=>110011101010101000
111001010101010100=>011110101010101000
111111110000000010=>000000011111111100
101111111100000000=>110000000001111111
111111101000000010=>111111110000000100
101111111010000000=>110111111100000000
111111100100000010=>011111111000000100
111111011000000010=>111111100000001100
101111111001000000=>110011111110000000
101111110110000000=>110111111000000001
10101010101010101010=>11010101010101010100
10101010101010101100=>11010101010101010001
10101010101010110100=>11010101010101011000
10101010101011010100=>11010101010101101000
10101010101101010100=>11010101010110101000
10101010110101010100=>11010101011010101000
10101011010101010100=>11010101101010101000
10101101010101010100=>11010110101010101000
10110101010101010100=>11011010101010101000
11010101010101010100=>11101010101010101000
11111111100000000010=>00000000111111111100
10111111111000000000=>11000000000011111111
11111111010000000010=>11111111100000000100
10111111110100000000=>11011111111000000000
1111111111000000000010=>0000000001111111111100
1011111111110000000000=>1100000000000111111111
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 an order ideal in the product of two chains.
In particular, this operation preserves the number of ones, and its order is the length of the word, see section 3.3 of [1].
In particular, this operation preserves the number of ones, and its order is the length of the word, see section 3.3 of [1].
References
[1] , Propp, J., Roby, T. Homomesy in products of two chains MathSciNet:3367853 arXiv:1310.5201
Properties
bijective, graded
Sage code
def mapping(w): if len(w) <= 1: return w r_w = [] factor = [] i = 0 while i < len(w): if i + 1 < len(w) and (not w[i] and w[i+1]): r_w.extend(reversed(factor)) factor = [] r_w.extend([1, 0]) i += 2 else: factor.append(w[i]) i += 1 r_w.extend(reversed(factor)) return Word(r_w)
Weight
40
Created
Jan 07, 2023 at 17:42 by Martin Rubey
Updated
Jan 07, 2023 at 17:42 by Martin Rubey
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