Identifier
- St000392: Binary words ⟶ ℤ
Values
=>
0=>0
1=>1
00=>0
01=>1
10=>1
11=>2
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111=>3
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011101000101=>3
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001011101100=>3
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100101010101=>1
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100101100101=>2
100101101001=>2
100101110001=>3
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100110101001=>2
100111000101=>3
100111001001=>3
100111010001=>3
101001010101=>1
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101010011001=>2
101010100101=>1
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101011001001=>2
101011100001=>3
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101100101001=>2
101101000101=>2
101101001001=>2
101101010001=>2
101110001001=>3
101110100001=>3
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110001011001=>2
110001100101=>2
110001101001=>2
110001110001=>3
110010010101=>2
110010011001=>2
110010100101=>2
110010101001=>2
110010110001=>2
110011000101=>2
110011001001=>2
110011010001=>2
110011100001=>3
110100010101=>2
110100011001=>2
110100100101=>2
110100101001=>2
110100110001=>2
110101000101=>2
110101001001=>2
110101010001=>2
110101100001=>2
110110000101=>2
110110001001=>2
110110010001=>2
110110100001=>2
110111000001=>3
111000010101=>3
111000101001=>3
111001000101=>3
111001001001=>3
111001010001=>3
111010001001=>3
111010100001=>3
111100000101=>4
111100001001=>4
111100010001=>4
111100100001=>4
111101000001=>4
10110111100000=>4
10111011010000=>3
10111011100000=>3
10111100110000=>4
10111101001000=>4
10111101010000=>4
10111101100000=>4
10111110000100=>5
10111110001000=>5
10111110010000=>5
10111110100000=>5
10111111000000=>6
11001111100000=>5
11011110000010=>4
11101101000010=>3
11101110000010=>3
11110011000010=>4
11110100100010=>4
11110101000010=>4
11110110000010=>4
11111000001100=>5
11111000010010=>5
11111000100010=>5
11111001000010=>5
11111010000010=>5
11111100000010=>6
1011110111000000=>4
1011111010100000=>5
1011111011000000=>5
1011111100010000=>6
1011111100100000=>6
1011111101000000=>6
1011111110000000=>7
1111011100000010=>4
1111101010000010=>5
1111101100000010=>5
1111110001000010=>6
1111110010000010=>6
1111110100000010=>6
1111111000000010=>7
111111110000000010=>8
101111111100000000=>8
111111101000000010=>7
101111111010000000=>7
111111100100000010=>7
111111011000000010=>6
101111111001000000=>7
101111110110000000=>6
11111111100000000010=>9
10111111111000000000=>9
11111111010000000010=>8
10111111110100000000=>8
1111111111000000000010=>10
1011111111110000000000=>10
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Description
The length of the longest run of ones in a binary word.
References
[1] Triangular array read by rows: T(n,k) = number of binary vectors of length n whose longest run of consecutive 1's has length k, for n >= 0, 0 <= k <= n. OEIS:A048004
Code
def statistic(w): if len(w) == 0: return 0 if w[0] == 1: c = Composition(w.delta())[::2] else: c = Composition(w.delta())[1::2] return max(c + [0])
Created
Feb 12, 2016 at 22:11 by Martin Rubey
Updated
Dec 12, 2017 at 14:52 by Martin Rubey
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