Identifier
- St001436: Binary words ⟶ ℤ
Values
=>
0=>0
1=>0
00=>0
01=>0
10=>1
11=>0
000=>0
001=>0
010=>1
011=>0
100=>2
101=>1
110=>2
111=>0
0000=>0
0001=>0
0010=>1
0011=>0
0100=>2
0101=>0
0110=>1
0111=>0
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1001=>2
1010=>1
1011=>1
1100=>3
1101=>2
1110=>3
1111=>0
00000=>0
00001=>0
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00100=>2
00101=>0
00110=>1
00111=>0
01000=>3
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01110=>1
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10000=>4
10001=>3
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10100=>4
10101=>2
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001110=>1
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100000=>5
100001=>4
100010=>4
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100101=>3
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0000000=>0
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1101101=>4
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1111000=>6
1111001=>5
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00000000=>0
00000001=>0
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11110000=>7
11110001=>6
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11110110=>7
11110111=>4
11111000=>7
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11111010=>7
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11111111=>0
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100010101=>5
100010110=>5
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100011000=>7
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100011010=>5
100011011=>4
100011100=>5
100011101=>4
100011110=>4
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110111101=>5
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111000010=>8
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111000101=>7
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111001000=>8
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111001010=>8
111001011=>6
111001100=>8
111001101=>7
111001110=>7
111001111=>4
111010000=>8
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111010010=>8
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111010100=>8
111010101=>7
111010110=>8
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111011000=>8
111011001=>7
111011010=>8
111011011=>6
111011100=>8
111011101=>6
111011110=>7
111011111=>3
111100000=>8
111100001=>7
111100010=>8
111100011=>6
111100100=>8
111100101=>7
111100110=>8
111100111=>5
111101000=>8
111101001=>7
111101010=>8
111101011=>6
111101100=>8
111101101=>7
111101110=>8
111101111=>4
111110000=>8
111110001=>7
111110010=>8
111110011=>6
111110100=>8
111110101=>7
111110110=>8
111110111=>5
111111000=>8
111111001=>7
111111010=>8
111111011=>6
111111100=>8
111111101=>7
111111110=>8
111111111=>0
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Description
The index of a given binary word in the lex-order among all its cyclic shifts.
References
[1] Ahlbach, C., Swanson, J. P. Refined cyclic sieving on words for the major index statistic MathSciNet:3836732
Code
def statistic(w): orbit = [ tuple(w[i:] + w[:i]) for i in range(len(w)) ] return sorted(set(orbit)).index(tuple(w))
Created
Jul 02, 2019 at 10:59 by Christian Stump
Updated
Jul 02, 2019 at 10:59 by Christian Stump
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