Identifier
- St001355: Binary words ⟶ ℤ
Values
=>
0=>0
1=>0
00=>0
01=>1
10=>1
11=>0
000=>0
001=>0
010=>1
011=>1
100=>1
101=>1
110=>0
111=>0
0000=>0
0001=>0
0010=>0
0011=>1
0100=>1
0101=>2
0110=>2
0111=>1
1000=>1
1001=>2
1010=>2
1011=>1
1100=>1
1101=>0
1110=>0
1111=>0
00000=>0
00001=>0
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00011=>0
00100=>0
00101=>0
00110=>1
00111=>1
01000=>1
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01011=>2
01100=>2
01101=>2
01110=>1
01111=>1
10000=>1
10001=>1
10010=>2
10011=>2
10100=>2
10101=>2
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10111=>1
11000=>1
11001=>1
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11011=>0
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11110=>0
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000000=>0
000001=>0
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000101=>0
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001100=>1
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001110=>2
001111=>1
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010001=>1
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010100=>2
010101=>3
010110=>3
010111=>2
011000=>2
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011111=>1
100000=>1
100001=>1
100010=>1
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100100=>2
100101=>3
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101111=>1
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110001=>2
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110011=>1
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110110=>0
110111=>0
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111110=>0
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0000000=>0
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0101000=>2
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1110000=>1
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1111000=>0
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00000000=>0
00000001=>0
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11110000=>1
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11111111=>0
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011110101=>1
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011110111=>1
011111000=>1
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100000000=>1
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100001000=>1
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100001011=>1
100001100=>1
100001101=>1
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100001111=>2
100010000=>1
100010001=>1
100010010=>1
100010011=>1
100010100=>1
100010101=>1
100010110=>2
100010111=>2
100011000=>2
100011001=>2
100011010=>3
100011011=>3
100011100=>3
100011101=>3
100011110=>2
100011111=>2
100100000=>2
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100100010=>2
100100011=>2
100100100=>2
100100101=>2
100100110=>3
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100101101=>4
100101110=>3
100101111=>3
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100111011=>2
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100111111=>2
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110111100=>0
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111000000=>1
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111000011=>2
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111011101=>0
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111100001=>1
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111100101=>0
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111101000=>0
111101001=>0
111101010=>0
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111101100=>0
111101101=>0
111101110=>0
111101111=>0
111110000=>0
111110001=>0
111110010=>0
111110011=>0
111110100=>0
111110101=>0
111110110=>0
111110111=>0
111111000=>0
111111001=>0
111111010=>0
111111011=>0
111111100=>0
111111101=>0
111111110=>0
111111111=>0
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Description
Number of non-empty prefixes of a binary word that contain equally many 0's and 1's.
Graphically, this is the number of returns to the main diagonal of the monotone lattice path of a binary word.
Graphically, this is the number of returns to the main diagonal of the monotone lattice path of a binary word.
Code
def statistic(P): return sum(1 for i in range(2,len(P)+1,2) if P[:i].count(0) == P[:i].count(1) )
Created
Feb 11, 2019 at 18:21 by Christian Stump
Updated
Feb 12, 2019 at 07:43 by Christian Stump
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