Identifier
Images
=>
=>
0=>0
1=>1
00=>00
01=>01
10=>01
11=>11
000=>000
001=>001
010=>001
011=>011
100=>001
101=>011
110=>011
111=>111
0000=>0000
0001=>0001
0010=>0001
0011=>0011
0100=>0001
0101=>0101
0110=>0011
0111=>0111
1000=>0001
1001=>0011
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1011=>0111
1100=>0011
1101=>0111
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1111=>1111
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00001=>00001
00010=>00001
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00101=>00101
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10100=>00011
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10111=>01111
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11101011000100=>00000101011111
11101011001000=>00000101011111
11101011010000=>00000101011111
11101011100000=>00000010111111
11101100010100=>00000101011111
11101100011000=>00000011011111
11101100100100=>00001001011111
11101100101000=>00000101011111
11101100110000=>00000011011111
11101101000010=>00000101011111
11101101000100=>00000101011111
11101101001000=>00000101011111
11101101010000=>00000101011111
11101101100000=>00000011011111
11101110000010=>00000010111111
11101110000100=>00000010111111
11101110001000=>00000010111111
11101110010000=>00000010111111
11101110100000=>00000010111111
11101111000000=>00000001111111
11110001010100=>00000101011111
11110001011000=>00000010111111
11110001100100=>00000110011111
11110001101000=>00000011011111
11110001110000=>00000001111111
11110010010100=>00001001011111
11110010011000=>00000100111111
11110010100100=>00001001011111
11110010101000=>00000101011111
11110010110000=>00000010111111
11110011000010=>00000100111111
11110011000100=>00000100111111
11110011001000=>00000100111111
11110011010000=>00000011011111
11110011100000=>00000001111111
11110100010100=>00000101011111
11110100011000=>00000011011111
11110100100010=>00001001011111
11110100100100=>00001001011111
11110100101000=>00000101011111
11110100110000=>00000011011111
11110101000010=>00000101011111
11110101000100=>00000101011111
11110101001000=>00000101011111
11110101010000=>00000101011111
11110101100000=>00000010111111
11110110000010=>00000010111111
11110110000100=>00000010111111
11110110001000=>00000010111111
11110110010000=>00000010111111
11110110100000=>00000010111111
11110111000000=>00000001111111
11111000001100=>00000001111111
11111000010010=>00000100111111
11111000010100=>00000010111111
11111000011000=>00000001111111
11111000100010=>00001000111111
11111000100100=>00000100111111
11111000101000=>00000010111111
11111000110000=>00000001111111
11111001000010=>00000100111111
11111001000100=>00000100111111
11111001001000=>00000100111111
11111001010000=>00000010111111
11111001100000=>00000001111111
11111010000010=>00000010111111
11111010000100=>00000010111111
11111010001000=>00000010111111
11111010010000=>00000010111111
11111010100000=>00000010111111
11111011000000=>00000001111111
11111100000010=>00000001111111
11111100000100=>00000001111111
11111100001000=>00000001111111
11111100010000=>00000001111111
11111100100000=>00000001111111
11111101000000=>00000001111111
11111110000000=>00000001111111
1010101010101010=>0010101010101011
1010101010101100=>0001010101010111
1010101010110100=>0001010101010111
1010101010111000=>0000101010101111
1010101011010100=>0001010101010111
1010101011100100=>0000101010101111
1010101011101000=>0000101010101111
1010101011110000=>0000010101011111
1010101101010100=>0001010101010111
1010101110010100=>0000101010101111
1010101110100100=>0000101010101111
1010101111000100=>0000010101011111
1010110101010100=>0001010101010111
1010111001010100=>0000101010101111
1010111010010100=>0000101010101111
1010111100010100=>0000010101011111
1011010101010100=>0001010101010111
1011100101010100=>0000101010101111
1011101001010100=>0000101010101111
1011110001010100=>0000010101011111
1011110111000000=>0000000111011111
1011111010100000=>0000001010111111
1011111011000000=>0000000110111111
1011111100010000=>0000000101111111
1011111100100000=>0000000101111111
1011111101000000=>0000000101111111
1011111110000000=>0000000011111111
1101010101010100=>0001010101010111
1110010101010100=>0000101010101111
1110100101010100=>0000101010101111
1111000101010100=>0000010101011111
1111011100000010=>0000000101111111
1111101010000010=>0000001010111111
1111101100000010=>0000000101111111
1111110001000010=>0000010001111111
1111110010000010=>0000001001111111
1111110100000010=>0000000101111111
1111111000000010=>0000000011111111
101010101010101010=>001010101010101011
101010101010101100=>000101010101010111
101010101010110100=>000101010101010111
101010101011010100=>000101010101010111
101010101101010100=>000101010101010111
101010110101010100=>000101010101010111
101011010101010100=>000101010101010111
101101010101010100=>000101010101010111
110101010101010100=>000101010101010111
101010101010111000=>000010101010101111
101010101011100100=>000010101010101111
101010101110010100=>000010101010101111
101010111001010100=>000010101010101111
101011100101010100=>000010101010101111
101110010101010100=>000010101010101111
111001010101010100=>000010101010101111
111111110000000010=>000000000111111111
101111111100000000=>000000000111111111
111111101000000010=>000000001011111111
101111111010000000=>000000001011111111
111111100100000010=>000000010011111111
111111011000000010=>000000001011111111
101111111001000000=>000000001011111111
101111110110000000=>000000001101111111
10101010101010101010=>00101010101010101011
10101010101010101100=>00010101010101010111
10101010101010110100=>00010101010101010111
10101010101011010100=>00010101010101010111
10101010101101010100=>00010101010101010111
10101010110101010100=>00010101010101010111
10101011010101010100=>00010101010101010111
10101101010101010100=>00010101010101010111
10110101010101010100=>00010101010101010111
11010101010101010100=>00010101010101010111
11111111100000000010=>00000000001111111111
10111111111000000000=>00000000001111111111
11111111010000000010=>00000000010111111111
10111111110100000000=>00000000010111111111
1111111111000000000010=>0000000000011111111111
1011111111110000000000=>0000000000011111111111
click to show experimental identities
(only identities of compositions of up to three maps are shown)
Description
The word obtained by sorting the weakly increasing runs lexicographically.
References
[1] Alexandersson, P., Nabawanda, O. Peaks are preserved under run-sorting arXiv:2104.04220
Properties
idempotent, graded
Sage code
def mapping(w): runs = [] last = None run = [] for l in w: if last is not None and last > l: runs.append(run) run = [] run.append(l) last = l runs.append(run) runs.sort() return Words([0,1], len(w))([l for run in runs for l in run])
Weight
40
Created
Apr 12, 2021 at 17:42 by Martin Rubey
Updated
Apr 12, 2021 at 17:42 by Martin Rubey
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