Identifier
- St001437: Binary words ⟶ ℤ
Values
=>
0=>1
1=>1
00=>2
01=>1
10=>2
11=>2
000=>3
001=>1
010=>2
011=>1
100=>3
101=>2
110=>3
111=>3
0000=>4
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1101=>3
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101110011000=>9
101110100010=>10
101110100100=>10
101110101000=>10
101110110000=>9
101111000010=>9
101111000100=>9
101111001000=>9
101111010000=>9
101111100000=>8
110010101010=>12
110010101100=>11
110010110010=>12
110010110100=>11
110010111000=>11
110011001010=>12
110011001100=>12
110011010010=>11
110011010100=>11
110011011000=>11
110011100010=>11
110011100100=>11
110011101000=>10
110011110000=>10
110100101010=>12
110100101100=>12
110100110010=>12
110100110100=>12
110100111000=>11
110101001010=>12
110101001100=>12
110101010010=>12
110101010100=>12
110101011000=>12
110101100010=>12
110101100100=>12
110101101000=>12
110101110000=>11
110110001010=>12
110110001100=>12
110110010010=>12
110110010100=>12
110110011000=>12
110110100010=>12
110110100100=>12
110110101000=>12
110110110000=>12
110111000010=>11
110111000100=>11
110111001000=>11
110111010000=>11
110111100000=>10
111000101010=>12
111000101100=>12
111000110010=>12
111000110100=>12
111000111000=>12
111001001010=>12
111001001100=>12
111001010010=>12
111001010100=>12
111001011000=>12
111001100010=>12
111001100100=>12
111001101000=>12
111001110000=>12
111010001010=>12
111010001100=>12
111010010010=>12
111010010100=>12
111010011000=>12
111010100010=>12
111010100100=>12
111010101000=>12
111010110000=>12
111011000010=>12
111011000100=>12
111011001000=>12
111011010000=>12
111011100000=>12
111100001010=>12
111100001100=>12
111100010010=>12
111100010100=>12
111100011000=>12
111100100010=>12
111100100100=>12
111100101000=>12
111100110000=>12
111101000010=>12
111101000100=>12
111101001000=>12
111101010000=>12
111101100000=>12
111110000010=>12
111110000100=>12
111110001000=>12
111110010000=>12
111110100000=>12
111111000000=>12
100001111100=>7
10110111100000=>9
10111011010000=>11
10111011100000=>10
10111100110000=>10
10111101001000=>11
10111101010000=>11
10111101100000=>10
10111110000100=>10
10111110001000=>10
10111110010000=>10
10111110100000=>10
10111111000000=>9
11001111100000=>11
11011110000010=>12
11101101000010=>14
11101110000010=>14
11110011000010=>14
11110100100010=>14
11110101000010=>14
11110110000010=>14
11111000001100=>14
11111000010010=>14
11111000100010=>14
11111001000010=>14
11111010000010=>14
11111100000010=>14
1011110111000000=>11
1011111010100000=>12
1011111011000000=>11
1011111100010000=>11
1011111100100000=>11
1011111101000000=>11
1011111110000000=>10
1111011100000010=>16
1111101010000010=>16
1111101100000010=>16
1111110001000010=>16
1111110010000010=>16
1111110100000010=>16
1111111000000010=>16
search for individual values
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Description
References
[1] Ahlbach, C., Swanson, J. P. Refined cyclic sieving on words for the major index statistic MathSciNet:3836732
Code
def lex(w):
orbit = [ tuple(w[i:] + w[:i]) for i in range(len(w)) ]
return sorted(set(orbit)).index(tuple(w))+1
def freq(w):
w = list(w)
n = len(w)
for i in sorted(Integer(n).divisors()):
if w == w[:i]*(n//i):
return n // i
def statistic(w):
return lex(w)*freq(w)
Created
Jul 02, 2019 at 11:52 by Christian Stump
Updated
Jul 04, 2019 at 22:29 by Martin Rubey
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