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
1000 => 3
1001 => 2
1010 => 1
1011 => 1
1100 => 3
1101 => 2
1110 => 3
1111 => 0
00000 => 0
00001 => 0
00010 => 1
00011 => 0
00100 => 2
00101 => 0
00110 => 1
00111 => 0
01000 => 3
01001 => 1
01010 => 2
01011 => 0
01100 => 2
01101 => 1
01110 => 1
01111 => 0
10000 => 4
10001 => 3
10010 => 3
10011 => 2
10100 => 4
10101 => 2
10110 => 3
10111 => 1
11000 => 4
11001 => 3
11010 => 4
11011 => 2
11100 => 4
11101 => 3
11110 => 4
11111 => 0
000000 => 0
000001 => 0
000010 => 1
000011 => 0
000100 => 2
000101 => 0
000110 => 1
000111 => 0
001000 => 3
001001 => 0
001010 => 1
001011 => 0
001100 => 2
001101 => 0
001110 => 1
001111 => 0
010000 => 4
010001 => 2
010010 => 1
010011 => 1
010100 => 3
010101 => 0
010110 => 1
010111 => 0
011000 => 3
011001 => 2
011010 => 2
011011 => 0
011100 => 2
011101 => 1
011110 => 1
011111 => 0
100000 => 5
100001 => 4
100010 => 4
100011 => 3
100100 => 2
100101 => 3
100110 => 3
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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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