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Your data matches 4 different statistics following compositions of up to 3 maps.
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Matching statistic: St000981
(load all 10 compositions to match this statistic)
(load all 10 compositions to match this statistic)
St000981: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
=> 4
[1,1,0,0]
=> 2
[1,0,1,0,1,0]
=> 6
[1,0,1,1,0,0]
=> 3
[1,1,0,0,1,0]
=> 3
[1,1,0,1,0,0]
=> 4
[1,1,1,0,0,0]
=> 2
[1,0,1,0,1,0,1,0]
=> 8
[1,0,1,0,1,1,0,0]
=> 5
[1,0,1,1,0,0,1,0]
=> 3
[1,0,1,1,0,1,0,0]
=> 4
[1,0,1,1,1,0,0,0]
=> 3
[1,1,0,0,1,0,1,0]
=> 5
[1,1,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,0,1,0]
=> 4
[1,1,0,1,0,1,0,0]
=> 6
[1,1,0,1,1,0,0,0]
=> 3
[1,1,1,0,0,0,1,0]
=> 3
[1,1,1,0,0,1,0,0]
=> 3
[1,1,1,0,1,0,0,0]
=> 4
[1,1,1,1,0,0,0,0]
=> 2
[1,0,1,0,1,0,1,0,1,0]
=> 10
[1,0,1,0,1,0,1,1,0,0]
=> 7
[1,0,1,0,1,1,0,0,1,0]
=> 5
[1,0,1,0,1,1,0,1,0,0]
=> 5
[1,0,1,0,1,1,1,0,0,0]
=> 5
[1,0,1,1,0,0,1,0,1,0]
=> 5
[1,0,1,1,0,0,1,1,0,0]
=> 3
[1,0,1,1,0,1,0,0,1,0]
=> 4
[1,0,1,1,0,1,0,1,0,0]
=> 6
[1,0,1,1,0,1,1,0,0,0]
=> 3
[1,0,1,1,1,0,0,0,1,0]
=> 3
[1,0,1,1,1,0,0,1,0,0]
=> 3
[1,0,1,1,1,0,1,0,0,0]
=> 4
[1,0,1,1,1,1,0,0,0,0]
=> 3
[1,1,0,0,1,0,1,0,1,0]
=> 7
[1,1,0,0,1,0,1,1,0,0]
=> 4
[1,1,0,0,1,1,0,0,1,0]
=> 3
[1,1,0,0,1,1,0,1,0,0]
=> 4
[1,1,0,0,1,1,1,0,0,0]
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> 5
[1,1,0,1,0,0,1,1,0,0]
=> 4
[1,1,0,1,0,1,0,0,1,0]
=> 6
[1,1,0,1,0,1,0,1,0,0]
=> 8
[1,1,0,1,0,1,1,0,0,0]
=> 5
[1,1,0,1,1,0,0,0,1,0]
=> 3
[1,1,0,1,1,0,0,1,0,0]
=> 3
[1,1,0,1,1,0,1,0,0,0]
=> 4
[1,1,0,1,1,1,0,0,0,0]
=> 3
[1,1,1,0,0,0,1,0,1,0]
=> 5
Description
The length of the longest zigzag subpath.
This is the length of the longest consecutive subpath that is a zigzag of the form $010...$ or of the form $101...$.
Matching statistic: St000982
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00158: Binary words —alternating inverse⟶ Binary words
St000982: Binary words ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 57%
Mp00104: Binary words —reverse⟶ Binary words
Mp00158: Binary words —alternating inverse⟶ Binary words
St000982: Binary words ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 57%
Values
[1,0,1,0]
=> 1010 => 0101 => 0000 => 4
[1,1,0,0]
=> 1100 => 0011 => 0110 => 2
[1,0,1,0,1,0]
=> 101010 => 010101 => 000000 => 6
[1,0,1,1,0,0]
=> 101100 => 001101 => 011000 => 3
[1,1,0,0,1,0]
=> 110010 => 010011 => 000110 => 3
[1,1,0,1,0,0]
=> 110100 => 001011 => 011110 => 4
[1,1,1,0,0,0]
=> 111000 => 000111 => 010010 => 2
[1,0,1,0,1,0,1,0]
=> 10101010 => 01010101 => 00000000 => 8
[1,0,1,0,1,1,0,0]
=> 10101100 => 00110101 => 01100000 => 5
[1,0,1,1,0,0,1,0]
=> 10110010 => 01001101 => 00011000 => 3
[1,0,1,1,0,1,0,0]
=> 10110100 => 00101101 => 01111000 => 4
[1,0,1,1,1,0,0,0]
=> 10111000 => 00011101 => 01001000 => 3
[1,1,0,0,1,0,1,0]
=> 11001010 => 01010011 => 00000110 => 5
[1,1,0,0,1,1,0,0]
=> 11001100 => 00110011 => 01100110 => 2
[1,1,0,1,0,0,1,0]
=> 11010010 => 01001011 => 00011110 => 4
[1,1,0,1,0,1,0,0]
=> 11010100 => 00101011 => 01111110 => 6
[1,1,0,1,1,0,0,0]
=> 11011000 => 00011011 => 01001110 => 3
[1,1,1,0,0,0,1,0]
=> 11100010 => 01000111 => 00010010 => 3
[1,1,1,0,0,1,0,0]
=> 11100100 => 00100111 => 01110010 => 3
[1,1,1,0,1,0,0,0]
=> 11101000 => 00010111 => 01000010 => 4
[1,1,1,1,0,0,0,0]
=> 11110000 => 00001111 => 01011010 => 2
[1,0,1,0,1,0,1,0,1,0]
=> 1010101010 => 0101010101 => 0000000000 => 10
[1,0,1,0,1,0,1,1,0,0]
=> 1010101100 => 0011010101 => 0110000000 => ? = 7
[1,0,1,0,1,1,0,0,1,0]
=> 1010110010 => 0100110101 => 0001100000 => 5
[1,0,1,0,1,1,0,1,0,0]
=> 1010110100 => 0010110101 => 0111100000 => ? = 5
[1,0,1,0,1,1,1,0,0,0]
=> 1010111000 => 0001110101 => 0100100000 => ? = 5
[1,0,1,1,0,0,1,0,1,0]
=> 1011001010 => 0101001101 => 0000011000 => 5
[1,0,1,1,0,0,1,1,0,0]
=> 1011001100 => 0011001101 => 0110011000 => ? = 3
[1,0,1,1,0,1,0,0,1,0]
=> 1011010010 => 0100101101 => 0001111000 => 4
[1,0,1,1,0,1,0,1,0,0]
=> 1011010100 => 0010101101 => 0111111000 => ? = 6
[1,0,1,1,0,1,1,0,0,0]
=> 1011011000 => 0001101101 => 0100111000 => ? = 3
[1,0,1,1,1,0,0,0,1,0]
=> 1011100010 => 0100011101 => 0001001000 => 3
[1,0,1,1,1,0,0,1,0,0]
=> 1011100100 => 0010011101 => 0111001000 => ? = 3
[1,0,1,1,1,0,1,0,0,0]
=> 1011101000 => 0001011101 => 0100001000 => ? = 4
[1,0,1,1,1,1,0,0,0,0]
=> 1011110000 => 0000111101 => 0101101000 => ? = 3
[1,1,0,0,1,0,1,0,1,0]
=> 1100101010 => 0101010011 => 0000000110 => 7
[1,1,0,0,1,0,1,1,0,0]
=> 1100101100 => 0011010011 => 0110000110 => ? = 4
[1,1,0,0,1,1,0,0,1,0]
=> 1100110010 => 0100110011 => 0001100110 => 3
[1,1,0,0,1,1,0,1,0,0]
=> 1100110100 => 0010110011 => 0111100110 => ? = 4
[1,1,0,0,1,1,1,0,0,0]
=> 1100111000 => 0001110011 => 0100100110 => ? = 2
[1,1,0,1,0,0,1,0,1,0]
=> 1101001010 => 0101001011 => 0000011110 => 5
[1,1,0,1,0,0,1,1,0,0]
=> 1101001100 => 0011001011 => 0110011110 => ? = 4
[1,1,0,1,0,1,0,0,1,0]
=> 1101010010 => 0100101011 => 0001111110 => 6
[1,1,0,1,0,1,0,1,0,0]
=> 1101010100 => 0010101011 => 0111111110 => ? = 8
[1,1,0,1,0,1,1,0,0,0]
=> 1101011000 => 0001101011 => 0100111110 => ? = 5
[1,1,0,1,1,0,0,0,1,0]
=> 1101100010 => 0100011011 => 0001001110 => 3
[1,1,0,1,1,0,0,1,0,0]
=> 1101100100 => 0010011011 => 0111001110 => ? = 3
[1,1,0,1,1,0,1,0,0,0]
=> 1101101000 => 0001011011 => 0100001110 => ? = 4
[1,1,0,1,1,1,0,0,0,0]
=> 1101110000 => 0000111011 => 0101101110 => ? = 3
[1,1,1,0,0,0,1,0,1,0]
=> 1110001010 => 0101000111 => 0000010010 => 5
[1,1,1,0,0,0,1,1,0,0]
=> 1110001100 => 0011000111 => 0110010010 => ? = 2
[1,1,1,0,0,1,0,0,1,0]
=> 1110010010 => 0100100111 => 0001110010 => 3
[1,1,1,0,0,1,0,1,0,0]
=> 1110010100 => 0010100111 => 0111110010 => ? = 5
[1,1,1,0,0,1,1,0,0,0]
=> 1110011000 => 0001100111 => 0100110010 => ? = 2
[1,1,1,0,1,0,0,0,1,0]
=> 1110100010 => 0100010111 => 0001000010 => 4
[1,1,1,0,1,0,0,1,0,0]
=> 1110100100 => 0010010111 => 0111000010 => ? = 4
[1,1,1,0,1,0,1,0,0,0]
=> 1110101000 => 0001010111 => 0100000010 => 6
[1,1,1,0,1,1,0,0,0,0]
=> 1110110000 => 0000110111 => 0101100010 => ? = 3
[1,1,1,1,0,0,0,0,1,0]
=> 1111000010 => 0100001111 => 0001011010 => 3
[1,1,1,1,0,0,0,1,0,0]
=> 1111000100 => 0010001111 => 0111011010 => ? = 3
[1,1,1,1,0,0,1,0,0,0]
=> 1111001000 => 0001001111 => 0100011010 => ? = 3
[1,1,1,1,0,1,0,0,0,0]
=> 1111010000 => 0000101111 => 0101111010 => ? = 4
[1,1,1,1,1,0,0,0,0,0]
=> 1111100000 => 0000011111 => 0101001010 => ? = 2
[1,0,1,0,1,0,1,0,1,0,1,0]
=> 101010101010 => 010101010101 => 000000000000 => ? = 12
[1,0,1,0,1,0,1,0,1,1,0,0]
=> 101010101100 => 001101010101 => 011000000000 => ? = 9
[1,0,1,0,1,0,1,1,0,0,1,0]
=> 101010110010 => 010011010101 => 000110000000 => ? = 7
[1,0,1,0,1,0,1,1,0,1,0,0]
=> 101010110100 => 001011010101 => 011110000000 => ? = 7
[1,0,1,0,1,0,1,1,1,0,0,0]
=> 101010111000 => 000111010101 => 010010000000 => ? = 7
[1,0,1,0,1,1,0,0,1,0,1,0]
=> 101011001010 => 010100110101 => 000001100000 => ? = 5
[1,0,1,0,1,1,0,0,1,1,0,0]
=> 101011001100 => 001100110101 => 011001100000 => ? = 5
[1,0,1,0,1,1,0,1,0,0,1,0]
=> 101011010010 => 010010110101 => 000111100000 => ? = 5
[1,0,1,0,1,1,0,1,0,1,0,0]
=> 101011010100 => 001010110101 => 011111100000 => 6
[1,0,1,0,1,1,0,1,1,0,0,0]
=> 101011011000 => 000110110101 => 010011100000 => ? = 5
[1,0,1,0,1,1,1,0,0,0,1,0]
=> 101011100010 => 010001110101 => 000100100000 => ? = 5
[1,0,1,0,1,1,1,0,0,1,0,0]
=> 101011100100 => 001001110101 => 011100100000 => ? = 5
[1,0,1,0,1,1,1,0,1,0,0,0]
=> 101011101000 => 000101110101 => 010000100000 => ? = 5
[1,0,1,0,1,1,1,1,0,0,0,0]
=> 101011110000 => 000011110101 => 010110100000 => ? = 5
[1,0,1,1,0,0,1,0,1,0,1,0]
=> 101100101010 => 010101001101 => 000000011000 => ? = 7
[1,0,1,1,0,0,1,0,1,1,0,0]
=> 101100101100 => 001101001101 => 011000011000 => ? = 4
[1,0,1,1,0,0,1,1,0,0,1,0]
=> 101100110010 => 010011001101 => 000110011000 => ? = 3
[1,0,1,1,0,0,1,1,0,1,0,0]
=> 101100110100 => 001011001101 => 011110011000 => 4
[1,0,1,1,0,0,1,1,1,0,0,0]
=> 101100111000 => 000111001101 => 010010011000 => ? = 3
[1,0,1,1,0,1,0,0,1,0,1,0]
=> 101101001010 => 010100101101 => 000001111000 => ? = 5
[1,0,1,1,0,1,0,0,1,1,0,0]
=> 101101001100 => 001100101101 => 011001111000 => 4
[1,0,1,1,0,1,0,1,0,0,1,0]
=> 101101010010 => 010010101101 => 000111111000 => 6
[1,0,1,1,0,1,0,1,0,1,0,0]
=> 101101010100 => 001010101101 => 011111111000 => ? = 8
[1,0,1,1,0,1,0,1,1,0,0,0]
=> 101101011000 => 000110101101 => 010011111000 => 5
[1,0,1,1,0,1,1,0,0,0,1,0]
=> 101101100010 => 010001101101 => 000100111000 => ? = 3
[1,0,1,1,0,1,1,0,0,1,0,0]
=> 101101100100 => 001001101101 => 011100111000 => 3
[1,0,1,1,0,1,1,0,1,0,0,0]
=> 101101101000 => 000101101101 => 010000111000 => ? = 4
[1,0,1,1,0,1,1,1,0,0,0,0]
=> 101101110000 => 000011101101 => 010110111000 => 3
[1,0,1,1,1,0,0,0,1,0,1,0]
=> 101110001010 => 010100011101 => 000001001000 => ? = 5
[1,0,1,1,1,0,0,0,1,1,0,0]
=> 101110001100 => 001100011101 => 011001001000 => ? = 3
[1,0,1,1,1,0,0,1,0,1,0,0]
=> 101110010100 => 001010011101 => 011111001000 => 5
[1,0,1,1,1,1,0,0,0,1,0,0]
=> 101111000100 => 001000111101 => 011101101000 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
=> 101111010000 => 000010111101 => 010111101000 => 4
[1,1,0,0,1,0,1,1,0,1,0,0]
=> 110010110100 => 001011010011 => 011110000110 => 4
[1,1,0,0,1,1,0,0,1,1,0,0]
=> 110011001100 => 001100110011 => 011001100110 => 2
[1,1,0,0,1,1,0,1,0,0,1,0]
=> 110011010010 => 010010110011 => 000111100110 => 4
[1,1,0,0,1,1,1,0,0,1,0,0]
=> 110011100100 => 001001110011 => 011100100110 => 3
Description
The length of the longest constant subword.
Matching statistic: St000983
(load all 9 compositions to match this statistic)
(load all 9 compositions to match this statistic)
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St000983: Binary words ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 43%
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St000983: Binary words ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 43%
Values
[1,0,1,0]
=> [1]
=> [1,0,1,0]
=> 1010 => 4
[1,1,0,0]
=> []
=> []
=> => ? = 2
[1,0,1,0,1,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> 101010 => 6
[1,0,1,1,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> 101100 => 3
[1,1,0,0,1,0]
=> [2]
=> [1,1,0,0,1,0]
=> 110010 => 3
[1,1,0,1,0,0]
=> [1]
=> [1,0,1,0]
=> 1010 => 4
[1,1,1,0,0,0]
=> []
=> []
=> => ? = 2
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> 10101010 => 8
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 5
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 10110010 => 3
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> 10110100 => 4
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 3
[1,1,0,0,1,0,1,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> 11001010 => 5
[1,1,0,0,1,1,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 2
[1,1,0,1,0,0,1,0]
=> [3,1]
=> [1,1,0,1,0,0,1,0]
=> 11010010 => 4
[1,1,0,1,0,1,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> 101010 => 6
[1,1,0,1,1,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> 101100 => 3
[1,1,1,0,0,0,1,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 11100010 => 3
[1,1,1,0,0,1,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> 110010 => 3
[1,1,1,0,1,0,0,0]
=> [1]
=> [1,0,1,0]
=> 1010 => 4
[1,1,1,1,0,0,0,0]
=> []
=> []
=> => ? = 2
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> [1,0,1,0,1,0,1,0,1,0]
=> 1010101010 => ? = 10
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 1010101100 => ? = 7
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [1,0,1,0,1,1,0,0,1,0]
=> 1010110010 => ? = 5
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 1010110100 => ? = 5
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1010111000 => ? = 5
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [1,0,1,1,0,0,1,0,1,0]
=> 1011001010 => ? = 5
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,0]
=> 1011001100 => ? = 3
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> [1,0,1,1,0,1,0,0,1,0]
=> 1011010010 => ? = 4
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> 1011010100 => ? = 6
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1011011000 => ? = 3
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1011100010 => ? = 3
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1011100100 => ? = 3
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> 1011101000 => ? = 4
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> 1011110000 => ? = 3
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [1,1,0,0,1,0,1,0,1,0]
=> 1100101010 => ? = 7
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [1,1,0,0,1,0,1,1,0,0]
=> 1100101100 => ? = 4
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,1,0,0,1,1,0,0,1,0]
=> 1100110010 => ? = 3
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [1,1,0,0,1,1,0,1,0,0]
=> 1100110100 => ? = 4
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> 1100111000 => ? = 2
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [1,1,0,1,0,0,1,0,1,0]
=> 1101001010 => ? = 5
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [1,1,0,1,0,0,1,1,0,0]
=> 1101001100 => ? = 4
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [1,1,0,1,0,1,0,0,1,0]
=> 1101010010 => ? = 6
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> 10101010 => 8
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 5
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> [1,1,0,1,1,0,0,0,1,0]
=> 1101100010 => ? = 3
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 10110010 => 3
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> 10110100 => 4
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 3
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1110001010 => ? = 5
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> 1110001100 => ? = 2
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1110010010 => ? = 3
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> 11001010 => 5
[1,1,1,0,0,1,1,0,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 2
[1,1,1,0,1,0,0,0,1,0]
=> [4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> 1110100010 => ? = 4
[1,1,1,0,1,0,0,1,0,0]
=> [3,1]
=> [1,1,0,1,0,0,1,0]
=> 11010010 => 4
[1,1,1,0,1,0,1,0,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> 101010 => 6
[1,1,1,0,1,1,0,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> 101100 => 3
[1,1,1,1,0,0,0,0,1,0]
=> [4]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1111000010 => ? = 3
[1,1,1,1,0,0,0,1,0,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 11100010 => 3
[1,1,1,1,0,0,1,0,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> 110010 => 3
[1,1,1,1,0,1,0,0,0,0]
=> [1]
=> [1,0,1,0]
=> 1010 => 4
[1,1,1,1,1,0,0,0,0,0]
=> []
=> []
=> => ? = 2
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> 101010101010 => ? = 12
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> 101010101100 => ? = 9
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> 101010110010 => ? = 7
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2,1]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> 101010110100 => ? = 7
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2,1]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> 101010111000 => ? = 7
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> 101011001010 => ? = 5
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> 101011001100 => ? = 5
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2,1]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> 101011010010 => ? = 5
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> 101011010100 => ? = 6
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> 101011011000 => ? = 5
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> 101011100010 => ? = 5
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> 101011100100 => ? = 5
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [3,2,2,2,1]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> 101011101000 => ? = 5
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2,1]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 101011110000 => ? = 5
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,1]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> 101100101010 => ? = 7
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> 101100101100 => ? = 4
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 101100110010 => ? = 3
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> 101100110100 => ? = 4
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> 10101010 => 8
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 5
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 10110010 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> 10110100 => 4
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 3
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> 11001010 => 5
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 2
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [3,1]
=> [1,1,0,1,0,0,1,0]
=> 11010010 => 4
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> 101010 => 6
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> 101100 => 3
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 11100010 => 3
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> 110010 => 3
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1]
=> [1,0,1,0]
=> 1010 => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> 10101010 => 8
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
=> [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 10110010 => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> 10110100 => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> 11001010 => 5
Description
The length of the longest alternating subword.
This is the length of the longest consecutive subword of the form $010...$ or of the form $101...$.
Matching statistic: St000381
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00039: Integer compositions —complement⟶ Integer compositions
St000381: Integer compositions ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 43%
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00039: Integer compositions —complement⟶ Integer compositions
St000381: Integer compositions ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 43%
Values
[1,0,1,0]
=> 1010 => [1,1,1,1] => [4] => 4
[1,1,0,0]
=> 1100 => [2,2] => [1,2,1] => 2
[1,0,1,0,1,0]
=> 101010 => [1,1,1,1,1,1] => [6] => 6
[1,0,1,1,0,0]
=> 101100 => [1,1,2,2] => [3,2,1] => 3
[1,1,0,0,1,0]
=> 110010 => [2,2,1,1] => [1,2,3] => 3
[1,1,0,1,0,0]
=> 110100 => [2,1,1,2] => [1,4,1] => 4
[1,1,1,0,0,0]
=> 111000 => [3,3] => [1,1,2,1,1] => 2
[1,0,1,0,1,0,1,0]
=> 10101010 => [1,1,1,1,1,1,1,1] => [8] => 8
[1,0,1,0,1,1,0,0]
=> 10101100 => [1,1,1,1,2,2] => [5,2,1] => 5
[1,0,1,1,0,0,1,0]
=> 10110010 => [1,1,2,2,1,1] => [3,2,3] => 3
[1,0,1,1,0,1,0,0]
=> 10110100 => [1,1,2,1,1,2] => [3,4,1] => 4
[1,0,1,1,1,0,0,0]
=> 10111000 => [1,1,3,3] => [3,1,2,1,1] => 3
[1,1,0,0,1,0,1,0]
=> 11001010 => [2,2,1,1,1,1] => [1,2,5] => 5
[1,1,0,0,1,1,0,0]
=> 11001100 => [2,2,2,2] => [1,2,2,2,1] => 2
[1,1,0,1,0,0,1,0]
=> 11010010 => [2,1,1,2,1,1] => [1,4,3] => 4
[1,1,0,1,0,1,0,0]
=> 11010100 => [2,1,1,1,1,2] => [1,6,1] => 6
[1,1,0,1,1,0,0,0]
=> 11011000 => [2,1,2,3] => [1,3,2,1,1] => 3
[1,1,1,0,0,0,1,0]
=> 11100010 => [3,3,1,1] => [1,1,2,1,3] => 3
[1,1,1,0,0,1,0,0]
=> 11100100 => [3,2,1,2] => [1,1,2,3,1] => 3
[1,1,1,0,1,0,0,0]
=> 11101000 => [3,1,1,3] => [1,1,4,1,1] => 4
[1,1,1,1,0,0,0,0]
=> 11110000 => [4,4] => [1,1,1,2,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0]
=> 1010101010 => [1,1,1,1,1,1,1,1,1,1] => [10] => ? = 10
[1,0,1,0,1,0,1,1,0,0]
=> 1010101100 => [1,1,1,1,1,1,2,2] => [7,2,1] => ? = 7
[1,0,1,0,1,1,0,0,1,0]
=> 1010110010 => [1,1,1,1,2,2,1,1] => [5,2,3] => ? = 5
[1,0,1,0,1,1,0,1,0,0]
=> 1010110100 => [1,1,1,1,2,1,1,2] => [5,4,1] => ? = 5
[1,0,1,0,1,1,1,0,0,0]
=> 1010111000 => [1,1,1,1,3,3] => [5,1,2,1,1] => ? = 5
[1,0,1,1,0,0,1,0,1,0]
=> 1011001010 => [1,1,2,2,1,1,1,1] => [3,2,5] => ? = 5
[1,0,1,1,0,0,1,1,0,0]
=> 1011001100 => [1,1,2,2,2,2] => [3,2,2,2,1] => ? = 3
[1,0,1,1,0,1,0,0,1,0]
=> 1011010010 => [1,1,2,1,1,2,1,1] => [3,4,3] => ? = 4
[1,0,1,1,0,1,0,1,0,0]
=> 1011010100 => [1,1,2,1,1,1,1,2] => [3,6,1] => ? = 6
[1,0,1,1,0,1,1,0,0,0]
=> 1011011000 => [1,1,2,1,2,3] => [3,3,2,1,1] => ? = 3
[1,0,1,1,1,0,0,0,1,0]
=> 1011100010 => [1,1,3,3,1,1] => [3,1,2,1,3] => ? = 3
[1,0,1,1,1,0,0,1,0,0]
=> 1011100100 => [1,1,3,2,1,2] => [3,1,2,3,1] => ? = 3
[1,0,1,1,1,0,1,0,0,0]
=> 1011101000 => [1,1,3,1,1,3] => [3,1,4,1,1] => ? = 4
[1,0,1,1,1,1,0,0,0,0]
=> 1011110000 => [1,1,4,4] => [3,1,1,2,1,1,1] => ? = 3
[1,1,0,0,1,0,1,0,1,0]
=> 1100101010 => [2,2,1,1,1,1,1,1] => [1,2,7] => ? = 7
[1,1,0,0,1,0,1,1,0,0]
=> 1100101100 => [2,2,1,1,2,2] => [1,2,4,2,1] => ? = 4
[1,1,0,0,1,1,0,0,1,0]
=> 1100110010 => [2,2,2,2,1,1] => [1,2,2,2,3] => ? = 3
[1,1,0,0,1,1,0,1,0,0]
=> 1100110100 => [2,2,2,1,1,2] => [1,2,2,4,1] => ? = 4
[1,1,0,0,1,1,1,0,0,0]
=> 1100111000 => [2,2,3,3] => [1,2,2,1,2,1,1] => ? = 2
[1,1,0,1,0,0,1,0,1,0]
=> 1101001010 => [2,1,1,2,1,1,1,1] => [1,4,5] => ? = 5
[1,1,0,1,0,0,1,1,0,0]
=> 1101001100 => [2,1,1,2,2,2] => [1,4,2,2,1] => ? = 4
[1,1,0,1,0,1,0,0,1,0]
=> 1101010010 => [2,1,1,1,1,2,1,1] => [1,6,3] => ? = 6
[1,1,0,1,0,1,0,1,0,0]
=> 1101010100 => [2,1,1,1,1,1,1,2] => [1,8,1] => 8
[1,1,0,1,0,1,1,0,0,0]
=> 1101011000 => [2,1,1,1,2,3] => [1,5,2,1,1] => ? = 5
[1,1,0,1,1,0,0,0,1,0]
=> 1101100010 => [2,1,2,3,1,1] => [1,3,2,1,3] => ? = 3
[1,1,0,1,1,0,0,1,0,0]
=> 1101100100 => [2,1,2,2,1,2] => [1,3,2,3,1] => ? = 3
[1,1,0,1,1,0,1,0,0,0]
=> 1101101000 => [2,1,2,1,1,3] => [1,3,4,1,1] => ? = 4
[1,1,0,1,1,1,0,0,0,0]
=> 1101110000 => [2,1,3,4] => [1,3,1,2,1,1,1] => ? = 3
[1,1,1,0,0,0,1,0,1,0]
=> 1110001010 => [3,3,1,1,1,1] => [1,1,2,1,5] => ? = 5
[1,1,1,0,0,0,1,1,0,0]
=> 1110001100 => [3,3,2,2] => [1,1,2,1,2,2,1] => ? = 2
[1,1,1,0,0,1,0,0,1,0]
=> 1110010010 => [3,2,1,2,1,1] => [1,1,2,3,3] => ? = 3
[1,1,1,0,0,1,0,1,0,0]
=> 1110010100 => [3,2,1,1,1,2] => [1,1,2,5,1] => ? = 5
[1,1,1,0,0,1,1,0,0,0]
=> 1110011000 => [3,2,2,3] => [1,1,2,2,2,1,1] => ? = 2
[1,1,1,0,1,0,0,0,1,0]
=> 1110100010 => [3,1,1,3,1,1] => [1,1,4,1,3] => ? = 4
[1,1,1,0,1,0,0,1,0,0]
=> 1110100100 => [3,1,1,2,1,2] => [1,1,4,3,1] => ? = 4
[1,1,1,0,1,0,1,0,0,0]
=> 1110101000 => [3,1,1,1,1,3] => [1,1,6,1,1] => ? = 6
[1,1,1,0,1,1,0,0,0,0]
=> 1110110000 => [3,1,2,4] => [1,1,3,2,1,1,1] => ? = 3
[1,1,1,1,0,0,0,0,1,0]
=> 1111000010 => [4,4,1,1] => [1,1,1,2,1,1,3] => ? = 3
[1,1,1,1,0,0,0,1,0,0]
=> 1111000100 => [4,3,1,2] => [1,1,1,2,1,3,1] => ? = 3
[1,1,1,1,0,0,1,0,0,0]
=> 1111001000 => [4,2,1,3] => [1,1,1,2,3,1,1] => ? = 3
[1,1,1,1,0,1,0,0,0,0]
=> 1111010000 => [4,1,1,4] => [1,1,1,4,1,1,1] => ? = 4
[1,1,1,1,1,0,0,0,0,0]
=> 1111100000 => [5,5] => [1,1,1,1,2,1,1,1,1] => ? = 2
[1,0,1,0,1,0,1,0,1,0,1,0]
=> 101010101010 => [1,1,1,1,1,1,1,1,1,1,1,1] => [12] => ? = 12
[1,0,1,0,1,0,1,0,1,1,0,0]
=> 101010101100 => [1,1,1,1,1,1,1,1,2,2] => [9,2,1] => ? = 9
[1,0,1,0,1,0,1,1,0,0,1,0]
=> 101010110010 => [1,1,1,1,1,1,2,2,1,1] => [7,2,3] => ? = 7
[1,0,1,0,1,0,1,1,0,1,0,0]
=> 101010110100 => [1,1,1,1,1,1,2,1,1,2] => [7,4,1] => ? = 7
[1,0,1,0,1,0,1,1,1,0,0,0]
=> 101010111000 => [1,1,1,1,1,1,3,3] => [7,1,2,1,1] => ? = 7
[1,0,1,0,1,1,0,0,1,0,1,0]
=> 101011001010 => [1,1,1,1,2,2,1,1,1,1] => [5,2,5] => ? = 5
[1,0,1,0,1,1,0,0,1,1,0,0]
=> 101011001100 => [1,1,1,1,2,2,2,2] => [5,2,2,2,1] => ? = 5
[1,0,1,0,1,1,0,1,0,0,1,0]
=> 101011010010 => [1,1,1,1,2,1,1,2,1,1] => [5,4,3] => ? = 5
[1,0,1,0,1,1,0,1,0,1,0,0]
=> 101011010100 => [1,1,1,1,2,1,1,1,1,2] => [5,6,1] => ? = 6
Description
The largest part of an integer composition.
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