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Your data matches 11 different statistics following compositions of up to 3 maps.
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Matching statistic: St000876
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
St000876: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00104: Binary words —reverse⟶ Binary words
St000876: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> 10 => 01 => 2
[1,0,1,0]
=> 1010 => 0101 => 3
[1,1,0,0]
=> 1100 => 0011 => 4
[1,0,1,0,1,0]
=> 101010 => 010101 => 3
[1,0,1,1,0,0]
=> 101100 => 001101 => 4
[1,1,0,0,1,0]
=> 110010 => 010011 => 4
[1,1,0,1,0,0]
=> 110100 => 001011 => 5
[1,1,1,0,0,0]
=> 111000 => 000111 => 6
[1,0,1,0,1,0,1,0]
=> 10101010 => 01010101 => 3
[1,0,1,0,1,1,0,0]
=> 10101100 => 00110101 => 4
[1,0,1,1,0,0,1,0]
=> 10110010 => 01001101 => 4
[1,0,1,1,0,1,0,0]
=> 10110100 => 00101101 => 5
[1,0,1,1,1,0,0,0]
=> 10111000 => 00011101 => 6
[1,1,0,0,1,0,1,0]
=> 11001010 => 01010011 => 4
[1,1,0,0,1,1,0,0]
=> 11001100 => 00110011 => 5
[1,1,0,1,0,0,1,0]
=> 11010010 => 01001011 => 5
[1,1,0,1,0,1,0,0]
=> 11010100 => 00101011 => 5
[1,1,0,1,1,0,0,0]
=> 11011000 => 00011011 => 6
[1,1,1,0,0,0,1,0]
=> 11100010 => 01000111 => 6
[1,1,1,0,0,1,0,0]
=> 11100100 => 00100111 => 6
[1,1,1,0,1,0,0,0]
=> 11101000 => 00010111 => 7
[1,1,1,1,0,0,0,0]
=> 11110000 => 00001111 => 8
[1,0,1,0,1,0,1,0,1,0]
=> 1010101010 => 0101010101 => 3
[1,0,1,0,1,0,1,1,0,0]
=> 1010101100 => 0011010101 => 4
[1,0,1,0,1,1,0,0,1,0]
=> 1010110010 => 0100110101 => 4
[1,0,1,0,1,1,0,1,0,0]
=> 1010110100 => 0010110101 => 5
[1,0,1,0,1,1,1,0,0,0]
=> 1010111000 => 0001110101 => 6
[1,0,1,1,0,0,1,0,1,0]
=> 1011001010 => 0101001101 => 4
[1,0,1,1,0,0,1,1,0,0]
=> 1011001100 => 0011001101 => 5
[1,0,1,1,0,1,0,0,1,0]
=> 1011010010 => 0100101101 => 5
[1,0,1,1,0,1,0,1,0,0]
=> 1011010100 => 0010101101 => 5
[1,0,1,1,0,1,1,0,0,0]
=> 1011011000 => 0001101101 => 6
[1,0,1,1,1,0,0,0,1,0]
=> 1011100010 => 0100011101 => 6
[1,0,1,1,1,0,0,1,0,0]
=> 1011100100 => 0010011101 => 6
[1,0,1,1,1,0,1,0,0,0]
=> 1011101000 => 0001011101 => 7
[1,0,1,1,1,1,0,0,0,0]
=> 1011110000 => 0000111101 => 8
[1,1,0,0,1,0,1,0,1,0]
=> 1100101010 => 0101010011 => 4
[1,1,0,0,1,0,1,1,0,0]
=> 1100101100 => 0011010011 => 5
[1,1,0,0,1,1,0,0,1,0]
=> 1100110010 => 0100110011 => 5
[1,1,0,0,1,1,0,1,0,0]
=> 1100110100 => 0010110011 => 5
[1,1,0,0,1,1,1,0,0,0]
=> 1100111000 => 0001110011 => 6
[1,1,0,1,0,0,1,0,1,0]
=> 1101001010 => 0101001011 => 5
[1,1,0,1,0,0,1,1,0,0]
=> 1101001100 => 0011001011 => 5
[1,1,0,1,0,1,0,0,1,0]
=> 1101010010 => 0100101011 => 5
[1,1,0,1,0,1,0,1,0,0]
=> 1101010100 => 0010101011 => 5
[1,1,0,1,0,1,1,0,0,0]
=> 1101011000 => 0001101011 => 6
[1,1,0,1,1,0,0,0,1,0]
=> 1101100010 => 0100011011 => 6
[1,1,0,1,1,0,0,1,0,0]
=> 1101100100 => 0010011011 => 6
[1,1,0,1,1,0,1,0,0,0]
=> 1101101000 => 0001011011 => 7
[1,1,0,1,1,1,0,0,0,0]
=> 1101110000 => 0000111011 => 8
Description
The number of factors in the Catalan decomposition of a binary word.
Every binary word can be written in a unique way as $(\mathcal D 0)^\ell \mathcal D (1 \mathcal D)^m$, where $\mathcal D$ is the set of Dyck words. This is the Catalan factorisation, see [1, sec.9.1.2].
This statistic records the number of factors in the Catalan factorisation, that is, $\ell + m$ if the middle Dyck word is empty and $\ell + 1 + m$ otherwise.
Matching statistic: St001500
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
Mp00143: Dyck paths —inverse promotion⟶ Dyck paths
St001500: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
Mp00143: Dyck paths —inverse promotion⟶ Dyck paths
St001500: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1 = 2 - 1
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,1,0,0,1,0]
=> [1,0,1,1,0,0]
=> 2 = 3 - 1
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [1,1,0,1,0,0]
=> 3 = 4 - 1
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> 4 = 5 - 1
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> [1,0,1,1,0,1,0,0]
=> 3 = 4 - 1
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> 2 = 3 - 1
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 3 = 4 - 1
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> 5 = 6 - 1
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> 6 = 7 - 1
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> 4 = 5 - 1
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 4 = 5 - 1
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 4 - 1
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> 5 = 6 - 1
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> 4 = 5 - 1
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> 3 = 4 - 1
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> 4 = 5 - 1
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> 5 = 6 - 1
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> 5 = 6 - 1
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> 2 = 3 - 1
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 3 = 4 - 1
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> 5 = 6 - 1
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 7 = 8 - 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> 8 = 9 - 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> 6 = 7 - 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> 6 = 7 - 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> 4 = 5 - 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> 5 = 6 - 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> 6 = 7 - 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> 4 = 5 - 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> 6 = 7 - 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> 5 = 6 - 1
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> 5 = 6 - 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 4 = 5 - 1
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> 3 = 4 - 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,1,0,0,1,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> 5 = 6 - 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> 7 = 8 - 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,1,0,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> 6 = 7 - 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,0,1,0,0]
=> 4 = 5 - 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 4 = 5 - 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,1,0,0,1,0,0]
=> 3 = 4 - 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> 5 = 6 - 1
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> 6 = 7 - 1
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> 4 = 5 - 1
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> 4 = 5 - 1
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> 5 = 6 - 1
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 7 = 8 - 1
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> 4 = 5 - 1
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> 5 = 6 - 1
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> 5 = 6 - 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> 7 = 8 - 1
Description
The global dimension of magnitude 1 Nakayama algebras.
We use the code below to translate them to Dyck paths.
Matching statistic: St000495
(load all 8 compositions to match this statistic)
(load all 8 compositions to match this statistic)
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00132: Dyck paths —switch returns and last double rise⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St000495: Permutations ⟶ ℤResult quality: 91% ●values known / values provided: 99%●distinct values known / distinct values provided: 91%
Mp00132: Dyck paths —switch returns and last double rise⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St000495: Permutations ⟶ ℤResult quality: 91% ●values known / values provided: 99%●distinct values known / distinct values provided: 91%
Values
[1,0]
=> [1,0]
=> [1,0]
=> [1] => ? = 2 - 3
[1,0,1,0]
=> [1,0,1,0]
=> [1,0,1,0]
=> [2,1] => 1 = 4 - 3
[1,1,0,0]
=> [1,1,0,0]
=> [1,1,0,0]
=> [1,2] => 0 = 3 - 3
[1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> [3,2,1] => 3 = 6 - 3
[1,0,1,1,0,0]
=> [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> [2,1,3] => 1 = 4 - 3
[1,1,0,0,1,0]
=> [1,1,0,0,1,0]
=> [1,1,0,0,1,0]
=> [3,1,2] => 2 = 5 - 3
[1,1,0,1,0,0]
=> [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> [2,1,3] => 1 = 4 - 3
[1,1,1,0,0,0]
=> [1,1,1,0,0,0]
=> [1,1,1,0,0,0]
=> [1,2,3] => 0 = 3 - 3
[1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 5 = 8 - 3
[1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,0]
=> [3,2,1,4] => 3 = 6 - 3
[1,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,0,1,0]
=> [4,2,1,3] => 3 = 6 - 3
[1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,0]
=> [3,2,1,4] => 3 = 6 - 3
[1,0,1,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> [2,1,3,4] => 1 = 4 - 3
[1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> [4,3,1,2] => 4 = 7 - 3
[1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> [3,1,2,4] => 2 = 5 - 3
[1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,0,1,0]
=> [4,2,1,3] => 3 = 6 - 3
[1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> [3,1,2,4] => 2 = 5 - 3
[1,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> [2,1,3,4] => 1 = 4 - 3
[1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,0]
=> [4,1,2,3] => 2 = 5 - 3
[1,1,1,0,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> [3,1,2,4] => 2 = 5 - 3
[1,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> [2,1,3,4] => 1 = 4 - 3
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,2,3,4] => 0 = 3 - 3
[1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => 7 = 10 - 3
[1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => 5 = 8 - 3
[1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => 5 = 8 - 3
[1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => 5 = 8 - 3
[1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => 3 = 6 - 3
[1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => 5 = 8 - 3
[1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => 3 = 6 - 3
[1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => 5 = 8 - 3
[1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => 3 = 6 - 3
[1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => 3 = 6 - 3
[1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,3,4] => 3 = 6 - 3
[1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => 3 = 6 - 3
[1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => 3 = 6 - 3
[1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [2,1,3,4,5] => 1 = 4 - 3
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => 6 = 9 - 3
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => 4 = 7 - 3
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => 4 = 7 - 3
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => 4 = 7 - 3
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => 2 = 5 - 3
[1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => 5 = 8 - 3
[1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => 3 = 6 - 3
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => 4 = 7 - 3
[1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => 3 = 6 - 3
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => 2 = 5 - 3
[1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,3,4] => 3 = 6 - 3
[1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => 3 = 6 - 3
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => 2 = 5 - 3
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [2,1,3,4,5] => 1 = 4 - 3
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => 4 = 7 - 3
Description
The number of inversions of distance at most 2 of a permutation.
An inversion of a permutation $\pi$ is a pair $i < j$ such that $\sigma(i) > \sigma(j)$. Let $j-i$ be the distance of such an inversion. Then inversions of distance at most 1 are then exactly the descents of $\pi$, see [[St000021]]. This statistic counts the number of inversions of distance at most 2.
Matching statistic: St000777
(load all 29 compositions to match this statistic)
(load all 29 compositions to match this statistic)
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 46% ●values known / values provided: 46%●distinct values known / distinct values provided: 55%
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 46% ●values known / values provided: 46%●distinct values known / distinct values provided: 55%
Values
[1,0]
=> [1] => [1] => ([],1)
=> 1 = 2 - 1
[1,0,1,0]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 2 = 3 - 1
[1,1,0,0]
=> [1,2] => [1,2] => ([],2)
=> ? = 4 - 1
[1,0,1,0,1,0]
=> [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 2 = 3 - 1
[1,0,1,1,0,0]
=> [2,3,1] => [2,3,1] => ([(0,2),(1,2)],3)
=> 3 = 4 - 1
[1,1,0,0,1,0]
=> [3,1,2] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {4,5,6} - 1
[1,1,0,1,0,0]
=> [2,1,3] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {4,5,6} - 1
[1,1,1,0,0,0]
=> [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {4,5,6} - 1
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 5 - 1
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 5 - 1
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 3 = 4 - 1
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,5,6,6,6,6,7,8} - 1
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 4 = 5 - 1
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? ∊ {4,5,6,6,6,6,7,8} - 1
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,5,6,6,6,6,7,8} - 1
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {4,5,6,6,6,6,7,8} - 1
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {4,5,6,6,6,6,7,8} - 1
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {4,5,6,6,6,6,7,8} - 1
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {4,5,6,6,6,6,7,8} - 1
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {4,5,6,6,6,6,7,8} - 1
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 3 - 1
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 4 - 1
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4 = 5 - 1
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4 = 5 - 1
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 4 - 1
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4 = 5 - 1
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [4,2,5,3,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 5 = 6 - 1
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 4 = 5 - 1
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4 = 5 - 1
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5 = 6 - 1
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 4 = 5 - 1
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 4 = 5 - 1
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 4 = 5 - 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 4 - 1
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 5 = 6 - 1
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 5 = 6 - 1
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [4,3,1,5,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 5 = 6 - 1
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 5 = 6 - 1
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 5 = 6 - 1
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [3,4,2,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,0,1,1,0,0,0]
=> [3,4,1,2,5] => [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,3,4] => [2,1,3,5,4] => ([(1,4),(2,3)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => [2,1,4,3,5] => ([(1,4),(2,3)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,1,1,0,0,0,0]
=> [2,3,1,4,5] => [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => [1,2,3,5,4] => ([(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,3,5] => [1,2,4,3,5] => ([(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => [1,3,2,4,5] => ([(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,1,0,1,0,0,0,0]
=> [2,1,3,4,5] => [2,1,3,4,5] => ([(3,4)],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => [1,2,3,4,5] => ([],5)
=> ? ∊ {4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [6,5,4,3,2,1] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [5,6,4,3,2,1] => [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 4 - 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,5,3,2,1] => [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4 = 5 - 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [5,4,6,3,2,1] => [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4 = 5 - 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [4,5,6,3,2,1] => [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 4 - 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,4,2,1] => [3,6,5,4,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4 = 5 - 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,6,3,4,2,1] => [5,3,6,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5 = 6 - 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,5,2,1] => [4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4 = 5 - 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [5,4,3,6,2,1] => [5,4,3,6,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4 = 5 - 1
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [4,5,3,6,2,1] => [4,5,3,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5 = 6 - 1
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [6,3,4,5,2,1] => [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4 = 5 - 1
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [5,3,4,6,2,1] => [3,5,4,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4 = 5 - 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [4,3,5,6,2,1] => [4,3,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4 = 5 - 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [3,4,5,6,2,1] => [3,4,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 4 - 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,3,1] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4 = 5 - 1
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,6,4,2,3,1] => [5,2,6,4,3,1] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,5,2,3,1] => [4,2,6,5,3,1] => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,6,2,3,1] => [5,4,2,6,3,1] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [4,5,6,2,3,1] => [4,5,2,6,3,1] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,4,1] => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5 = 6 - 1
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [5,6,3,2,4,1] => [5,3,2,6,4,1] => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [6,5,4,3,1,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,1,3] => [2,1,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,1,0,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,1,4] => [3,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,1,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,1,5] => [4,3,2,1,6,5] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2,1,6] => [5,4,3,2,1,6] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [4,5,3,2,1,6] => [4,5,3,2,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,1,0,1,0,1,1,0,0,0,1,0]
=> [6,3,4,2,1,5] => [3,4,2,1,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [5,3,4,2,1,6] => [3,5,4,2,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [4,3,5,2,1,6] => [4,3,5,2,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [3,4,5,2,1,6] => [3,4,5,2,1,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,1,0,1,1,0,0,0,1,0,1,0]
=> [6,5,2,3,1,4] => [2,3,1,6,5,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [6,4,2,3,1,5] => [2,4,3,1,6,5] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [5,4,2,3,1,6] => [2,5,4,3,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [4,5,2,3,1,6] => [4,2,5,3,1,6] => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [6,3,2,4,1,5] => [3,2,4,1,6,5] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St000259
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 33%●distinct values known / distinct values provided: 55%
Mp00160: Permutations —graph of inversions⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 33%●distinct values known / distinct values provided: 55%
Values
[1,0]
=> [1] => ([],1)
=> 0 = 2 - 2
[1,0,1,0]
=> [2,1] => ([(0,1)],2)
=> 1 = 3 - 2
[1,1,0,0]
=> [1,2] => ([],2)
=> ? = 4 - 2
[1,0,1,0,1,0]
=> [2,3,1] => ([(0,2),(1,2)],3)
=> 2 = 4 - 2
[1,0,1,1,0,0]
=> [2,1,3] => ([(1,2)],3)
=> ? ∊ {3,5,6} - 2
[1,1,0,0,1,0]
=> [1,3,2] => ([(1,2)],3)
=> ? ∊ {3,5,6} - 2
[1,1,0,1,0,0]
=> [3,1,2] => ([(0,2),(1,2)],3)
=> 2 = 4 - 2
[1,1,1,0,0,0]
=> [1,2,3] => ([],3)
=> ? ∊ {3,5,6} - 2
[1,0,1,0,1,0,1,0]
=> [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 4 - 2
[1,0,1,0,1,1,0,0]
=> [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {3,5,5,6,6,6,6,7,8} - 2
[1,0,1,1,0,0,1,0]
=> [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? ∊ {3,5,5,6,6,6,6,7,8} - 2
[1,0,1,1,0,1,0,0]
=> [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> 3 = 5 - 2
[1,0,1,1,1,0,0,0]
=> [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {3,5,5,6,6,6,6,7,8} - 2
[1,1,0,0,1,0,1,0]
=> [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? ∊ {3,5,5,6,6,6,6,7,8} - 2
[1,1,0,0,1,1,0,0]
=> [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {3,5,5,6,6,6,6,7,8} - 2
[1,1,0,1,0,0,1,0]
=> [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 3 = 5 - 2
[1,1,0,1,0,1,0,0]
=> [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 4 - 2
[1,1,0,1,1,0,0,0]
=> [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? ∊ {3,5,5,6,6,6,6,7,8} - 2
[1,1,1,0,0,0,1,0]
=> [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {3,5,5,6,6,6,6,7,8} - 2
[1,1,1,0,0,1,0,0]
=> [1,4,2,3] => ([(1,3),(2,3)],4)
=> ? ∊ {3,5,5,6,6,6,6,7,8} - 2
[1,1,1,0,1,0,0,0]
=> [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 4 - 2
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => ([],4)
=> ? ∊ {3,5,5,6,6,6,6,7,8} - 2
[1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 4 - 2
[1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,0,1,1,0,0,1,0]
=> [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,0,1,1,0,1,0,0]
=> [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3 = 5 - 2
[1,0,1,0,1,1,1,0,0,0]
=> [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,0,0,1,1,0,0]
=> [2,1,4,3,5] => ([(1,4),(2,3)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,0,1,0,0,1,0]
=> [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4 = 6 - 2
[1,0,1,1,0,1,0,1,0,0]
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 3 = 5 - 2
[1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,5,4] => ([(1,4),(2,3)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3 = 5 - 2
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => ([(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,0,1,0,1,0,1,0]
=> [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,0,1,0,1,1,0,0]
=> [1,3,4,2,5] => ([(2,4),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4] => ([(1,4),(2,3)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,0,1,1,0,1,0,0]
=> [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,0,1,1,1,0,0,0]
=> [1,3,2,4,5] => ([(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3 = 5 - 2
[1,1,0,1,0,0,1,1,0,0]
=> [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,1,0,1,0,0,1,0]
=> [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 3 = 5 - 2
[1,1,0,1,0,1,0,1,0,0]
=> [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 2 = 4 - 2
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4 = 6 - 2
[1,1,0,1,1,0,1,0,0,0]
=> [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 3 = 5 - 2
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => ([(2,4),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,0,0,1,0,1,0]
=> [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,0,0,1,1,0,0]
=> [1,2,4,3,5] => ([(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,0,1,0,0,1,0]
=> [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,2,3,5] => ([(2,4),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,1,0,0,0,1,0]
=> [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3 = 5 - 2
[1,1,1,0,1,0,0,1,0,0]
=> [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 3 = 5 - 2
[1,1,1,0,1,0,1,0,0,0]
=> [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 2 = 4 - 2
[1,1,1,0,1,1,0,0,0,0]
=> [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,1,0,0,0,0,1,0]
=> [1,2,3,5,4] => ([(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,1,0,0,0,1,0,0]
=> [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,1,0,0,1,0,0,0]
=> [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,1,0,1,0,0,0,0]
=> [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 4 - 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => ([],5)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [2,3,4,1,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> 3 = 5 - 2
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> 4 = 6 - 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 3 = 5 - 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [2,3,5,1,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [2,3,1,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 3 = 5 - 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,3,1,4,5,6] => ([(3,5),(4,5)],6)
=> ? ∊ {3,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> 4 = 6 - 2
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 6 - 2
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 3 = 5 - 2
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 5 = 7 - 2
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 3 = 5 - 2
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> 4 = 6 - 2
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> 4 = 6 - 2
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 3 = 5 - 2
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> 3 = 5 - 2
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [3,1,4,5,6,2] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> 3 = 5 - 2
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> 4 = 6 - 2
[1,1,0,1,0,1,0,0,1,0,1,0]
=> [3,4,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 3 = 5 - 2
[1,1,0,1,0,1,0,1,0,0,1,0]
=> [3,4,5,1,6,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 3 = 5 - 2
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 2 = 4 - 2
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> 4 = 6 - 2
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 3 = 5 - 2
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 5 = 7 - 2
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> 4 = 6 - 2
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> 4 = 6 - 2
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3 = 5 - 2
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 3 = 5 - 2
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> 4 = 6 - 2
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Matching statistic: St001880
(load all 7 compositions to match this statistic)
(load all 7 compositions to match this statistic)
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 28% ●values known / values provided: 28%●distinct values known / distinct values provided: 45%
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 28% ●values known / values provided: 28%●distinct values known / distinct values provided: 45%
Values
[1,0]
=> [1,1,0,0]
=> [1,2] => ([(0,1)],2)
=> ? = 2
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,3,2] => ([(0,1),(0,2)],3)
=> ? = 4
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {3,5,6}
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {3,5,6}
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ? ∊ {3,5,6}
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {3,4,5,6,6,6,6,7,8}
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ? ∊ {3,4,5,6,6,6,6,7,8}
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {3,4,5,6,6,6,6,7,8}
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,4,2,5,3] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ? ∊ {3,4,5,6,6,6,6,7,8}
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,4,5,2,3] => ([(0,3),(0,4),(3,2),(4,1)],5)
=> ? ∊ {3,4,5,6,6,6,6,7,8}
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ? ∊ {3,4,5,6,6,6,6,7,8}
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,5,2,3,4] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {3,4,5,6,6,6,6,7,8}
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,2,5,3,4] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ? ∊ {3,4,5,6,6,6,6,7,8}
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,2,3,5,4] => ([(0,3),(3,4),(4,1),(4,2)],5)
=> ? ∊ {3,4,5,6,6,6,6,7,8}
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,3,2,5,4,6] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,3,5,2,4,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,3,2,5,6,4] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,3,5,2,6,4] => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,3,5,6,2,4] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,3,2,6,4,5] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,3,6,2,4,5] => ([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,3,2,4,6,5] => ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,3,4,2,6,5] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,3,4,6,2,5] => ([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> 5
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 4
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,3,4,5,6,2] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,4,2,5,3,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> 4
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,4,2,5,6,3] => ([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,4,5,2,6,3] => ([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,4,5,6,2,3] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,4,2,6,3,5] => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,4,6,2,3,5] => ([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,4,2,3,6,5] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,2,4,3,6,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,2,4,6,3,5] => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,4,2,3,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> 5
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 5
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,2,4,5,6,3] => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,5,2,6,3,4] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,5,6,2,3,4] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,5,2,3,6,4] => ([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,2,5,3,6,4] => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,2,5,6,3,4] => ([(0,5),(3,2),(4,1),(5,3),(5,4)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 4
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 5
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,2,3,5,6,4] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,6,2,3,4,5] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,2,6,3,4,5] => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ? ∊ {3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,3,2,5,4,7,6] => ([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
=> ? ∊ {3,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12}
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [1,3,5,2,4,7,6] => ([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7)
=> ? ∊ {3,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [1,3,2,5,7,4,6] => ([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
=> ? ∊ {3,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12}
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [1,3,5,2,7,4,6] => ([(0,2),(0,3),(1,4),(1,6),(2,4),(2,5),(3,1),(3,5),(5,6)],7)
=> ? ∊ {3,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12}
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,3,5,7,2,4,6] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)
=> ? ∊ {3,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [1,3,2,5,4,6,7] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
=> ? ∊ {3,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12}
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [1,3,5,2,4,6,7] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> 7
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [1,3,2,5,6,4,7] => ([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)
=> ? ∊ {3,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12}
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [1,3,5,6,2,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> 6
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,1,1,0,0,0]
=> [1,3,6,2,4,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
=> 6
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> [1,3,2,4,6,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> 7
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> [1,3,4,6,2,5,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> 6
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=> [1,3,2,4,5,6,7] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> 7
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> [1,3,4,2,5,6,7] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
=> 6
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [1,3,4,5,2,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> 5
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [1,3,4,5,6,2,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> 4
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,1,0,0]
=> [1,4,2,5,3,6,7] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> 7
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,1,1,0,0,0]
=> [1,4,5,2,3,6,7] => ([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
=> 5
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,1,0,0,1,0,0]
=> [1,4,2,5,6,3,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
=> 6
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,1,0,0,0]
=> [1,4,5,2,6,3,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
=> 6
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [1,4,5,6,2,3,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> 4
[1,1,0,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,1,0,0,1,1,0,0,0]
=> [1,4,6,2,3,5,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
=> 6
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=> [1,2,4,6,3,5,7] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> 7
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,0]
=> [1,4,2,3,5,6,7] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
=> 6
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=> [1,2,4,3,5,6,7] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> 7
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,1,1,0,0,1,0,0,0,0]
=> [1,2,4,5,3,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> 6
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,1,0,0,0,0,0]
=> [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
=> 5
[1,1,1,0,0,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,1,0,0]
=> [1,5,2,6,3,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> 6
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=> [1,5,6,2,3,4,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> 4
[1,1,1,0,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,1,0,0,1,0,0]
=> [1,5,2,3,6,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> 6
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
=> [1,2,5,3,6,4,7] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> 7
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=> [1,2,5,6,3,4,7] => ([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
=> 5
[1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=> [1,5,2,3,4,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> 5
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,1,1,0,0,0,1,0,0,0]
=> [1,2,5,3,4,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> 6
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,1,1,0,0,1,0,0,0,0]
=> [1,2,3,5,4,6,7] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> 7
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> [1,2,3,5,6,4,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
=> 6
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St001914
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St001914: Integer partitions ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 64%
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St001914: Integer partitions ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 64%
Values
[1,0]
=> [1,0]
=> [1,0]
=> []
=> ? = 2
[1,0,1,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> []
=> ? ∊ {3,4}
[1,1,0,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> []
=> ? ∊ {3,4}
[1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> []
=> ? ∊ {3,4,4,5,6}
[1,0,1,1,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> []
=> ? ∊ {3,4,4,5,6}
[1,1,0,0,1,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> []
=> ? ∊ {3,4,4,5,6}
[1,1,0,1,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> []
=> ? ∊ {3,4,4,5,6}
[1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> []
=> ? ∊ {3,4,4,5,6}
[1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {4,4,4,5,5,5,5,6,6,6,6,7,8}
[1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {4,4,4,5,5,5,5,6,6,6,6,7,8}
[1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {4,4,4,5,5,5,5,6,6,6,6,7,8}
[1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {4,4,4,5,5,5,5,6,6,6,6,7,8}
[1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {4,4,4,5,5,5,5,6,6,6,6,7,8}
[1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {4,4,4,5,5,5,5,6,6,6,6,7,8}
[1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {4,4,4,5,5,5,5,6,6,6,6,7,8}
[1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {4,4,4,5,5,5,5,6,6,6,6,7,8}
[1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {4,4,4,5,5,5,5,6,6,6,6,7,8}
[1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {4,4,4,5,5,5,5,6,6,6,6,7,8}
[1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {4,4,4,5,5,5,5,6,6,6,6,7,8}
[1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {4,4,4,5,5,5,5,6,6,6,6,7,8}
[1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {4,4,4,5,5,5,5,6,6,6,6,7,8}
[1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> [2,2]
=> 3
[1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> 5
[1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> 5
[1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10}
[1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> 5
[1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> 4
[1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> 4
[1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> 4
[1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [2,2]
=> 3
[1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> 4
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [4,4]
=> 5
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [4,4]
=> 5
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [4,4]
=> 5
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> 8
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> 8
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> 8
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [3,3]
=> 5
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> [4,4,3]
=> 10
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [4,4]
=> 5
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [4,4]
=> 5
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [4,4]
=> 5
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> 8
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> 8
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> 8
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [3,3]
=> 5
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> [4,4,3]
=> 10
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [4,4]
=> 5
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [4,4]
=> 5
[1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> 8
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> 8
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> 8
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [3,3]
=> 5
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> [4,4,3]
=> 10
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2]
=> 5
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2]
=> 5
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2]
=> 5
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2]
=> 5
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2]
=> 5
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2]
=> 5
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2]
=> 5
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2]
=> 5
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2]
=> 5
[1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [2,2,2]
=> 4
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [2,2,2]
=> 4
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [2,2,2]
=> 4
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [2,2]
=> 3
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> 6
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2]
=> 9
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2]
=> 9
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2]
=> 9
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> 9
Description
The size of the orbit of an integer partition in Bulgarian solitaire.
Bulgarian solitaire is the dynamical system where a move consists of removing the first column of the Ferrers diagram and inserting it as a row.
This statistic returns the number of partitions that can be obtained from the given partition.
Matching statistic: St001232
(load all 11 compositions to match this statistic)
(load all 11 compositions to match this statistic)
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 64%
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 64%
Values
[1,0]
=> [1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1 = 2 - 1
[1,0,1,0]
=> [1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,0,1,1,0,0]
=> 2 = 3 - 1
[1,1,0,0]
=> [1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? = 4 - 1
[1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> 3 = 4 - 1
[1,0,1,1,0,0]
=> [1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> ? ∊ {3,5,6} - 1
[1,1,0,0,1,0]
=> [1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> 3 = 4 - 1
[1,1,0,1,0,0]
=> [1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> ? ∊ {3,5,6} - 1
[1,1,1,0,0,0]
=> [1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {3,5,6} - 1
[1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 4 = 5 - 1
[1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> ? ∊ {3,4,4,4,6,6,6,7,8} - 1
[1,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {3,4,4,4,6,6,6,7,8} - 1
[1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> ? ∊ {3,4,4,4,6,6,6,7,8} - 1
[1,0,1,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> ? ∊ {3,4,4,4,6,6,6,7,8} - 1
[1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 5 = 6 - 1
[1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 4 = 5 - 1
[1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {3,4,4,4,6,6,6,7,8} - 1
[1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 4 = 5 - 1
[1,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> ? ∊ {3,4,4,4,6,6,6,7,8} - 1
[1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {3,4,4,4,6,6,6,7,8} - 1
[1,1,1,0,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 4 = 5 - 1
[1,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> ? ∊ {3,4,4,4,6,6,6,7,8} - 1
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {3,4,4,4,6,6,6,7,8} - 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 6 - 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 5 = 6 - 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 5 = 6 - 1
[1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> 6 = 7 - 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,1,0,0]
=> ? ∊ {3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,1,0,0,0]
=> ? ∊ {3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,1,0,0]
=> ? ∊ {3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> ? ∊ {3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,1,0,0]
=> 7 = 8 - 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> 6 = 7 - 1
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> 6 = 7 - 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> 6 = 7 - 1
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> 6 = 7 - 1
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> 6 = 7 - 1
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,1,0,0]
=> 7 = 8 - 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> 6 = 7 - 1
[1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> 6 = 7 - 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> 6 = 7 - 1
[1,1,1,0,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> 7 = 8 - 1
[1,1,1,0,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> 7 = 8 - 1
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6 = 7 - 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001645
(load all 12 compositions to match this statistic)
(load all 12 compositions to match this statistic)
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 55%
Mp00126: Permutations —cactus evacuation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 55%
Values
[1,0]
=> [1] => [1] => ([],1)
=> 1 = 2 - 1
[1,0,1,0]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 2 = 3 - 1
[1,1,0,0]
=> [1,2] => [1,2] => ([],2)
=> ? = 4 - 1
[1,0,1,0,1,0]
=> [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
[1,0,1,1,0,0]
=> [2,3,1] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {3,4,6} - 1
[1,1,0,0,1,0]
=> [3,1,2] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {3,4,6} - 1
[1,1,0,1,0,0]
=> [2,1,3] => [2,3,1] => ([(0,2),(1,2)],3)
=> 4 = 5 - 1
[1,1,1,0,0,0]
=> [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {3,4,6} - 1
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 5 - 1
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {3,4,4,4,5,5,6,6,6,6,7,8} - 1
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {3,4,4,4,5,5,6,6,6,6,7,8} - 1
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {3,4,4,4,5,5,6,6,6,6,7,8} - 1
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {3,4,4,4,5,5,6,6,6,6,7,8} - 1
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {3,4,4,4,5,5,6,6,6,6,7,8} - 1
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4 = 5 - 1
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {3,4,4,4,5,5,6,6,6,6,7,8} - 1
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {3,4,4,4,5,5,6,6,6,6,7,8} - 1
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {3,4,4,4,5,5,6,6,6,6,7,8} - 1
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {3,4,4,4,5,5,6,6,6,6,7,8} - 1
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? ∊ {3,4,4,4,5,5,6,6,6,6,7,8} - 1
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {3,4,4,4,5,5,6,6,6,6,7,8} - 1
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {3,4,4,4,5,5,6,6,6,6,7,8} - 1
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5 = 6 - 1
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5 = 6 - 1
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [2,1,3,4,5] => ([(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 5 = 6 - 1
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [4,5,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5 = 6 - 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [3,4,2,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [2,5,3,4,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,0,1,1,0,0,0]
=> [3,4,1,2,5] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,3,4] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,0,1,1,0,0,0,0]
=> [2,3,1,4,5] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => [1,2,3,5,4] => ([(3,4)],5)
=> ? ∊ {3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [6,5,4,3,2,1] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,4,2,1] => [6,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,5,2,1] => [6,4,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,6,4,2,3,1] => [5,4,6,2,1,3] => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,5,2,3,1] => [6,4,5,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,6,2,3,1] => [5,4,6,2,3,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,4,1] => [6,3,5,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,5,1] => [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2,6,1] => [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [6,3,2,4,5,1] => [6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [5,6,4,3,1,2] => [5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [6,4,5,3,1,2] => [4,6,5,1,3,2] => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [5,4,6,3,1,2] => [5,6,4,1,3,2] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [5,6,3,4,1,2] => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 6 = 7 - 1
[1,1,0,1,0,0,1,0,1,1,0,0]
=> [5,6,4,2,1,3] => [5,6,4,2,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,5,2,1,3] => [4,6,5,2,3,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [5,4,6,2,1,3] => [5,6,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,1,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,1,5] => [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2,1,6] => [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [4,5,6,1,2,3] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> 6 = 7 - 1
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [4,5,3,1,2,6] => [4,5,6,3,1,2] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [4,3,5,1,2,6] => [4,5,6,1,3,2] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [4,5,2,1,3,6] => [4,5,6,2,1,3] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [4,3,2,1,5,6] => [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 7 - 1
Description
The pebbling number of a connected graph.
Matching statistic: St000691
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00280: Binary words —path rowmotion⟶ Binary words
St000691: Binary words ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 64%
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00280: Binary words —path rowmotion⟶ Binary words
St000691: Binary words ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 64%
Values
[1,0]
=> [1,0]
=> 10 => 11 => 0 = 2 - 2
[1,0,1,0]
=> [1,0,1,0]
=> 1010 => 1101 => 2 = 4 - 2
[1,1,0,0]
=> [1,1,0,0]
=> 1100 => 0111 => 1 = 3 - 2
[1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> 101010 => 110101 => 4 = 6 - 2
[1,0,1,1,0,0]
=> [1,0,1,1,0,0]
=> 101100 => 110011 => 2 = 4 - 2
[1,1,0,0,1,0]
=> [1,1,0,0,1,0]
=> 110010 => 011101 => 3 = 5 - 2
[1,1,0,1,0,0]
=> [1,0,1,1,0,0]
=> 101100 => 110011 => 2 = 4 - 2
[1,1,1,0,0,0]
=> [1,1,1,0,0,0]
=> 111000 => 001111 => 1 = 3 - 2
[1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> 10101010 => 11010101 => 6 = 8 - 2
[1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 11010011 => 4 = 6 - 2
[1,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> 10110010 => 11001101 => 4 = 6 - 2
[1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 11010011 => 4 = 6 - 2
[1,0,1,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 11000111 => 2 = 4 - 2
[1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> 11001010 => 01110101 => 5 = 7 - 2
[1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 01110011 => 3 = 5 - 2
[1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> 10110010 => 11001101 => 4 = 6 - 2
[1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 01110011 => 3 = 5 - 2
[1,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 11000111 => 2 = 4 - 2
[1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,0]
=> 11100010 => 00111101 => 3 = 5 - 2
[1,1,1,0,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 01110011 => 3 = 5 - 2
[1,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 11000111 => 2 = 4 - 2
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> 11110000 => 00011111 => 1 = 3 - 2
[1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> 1010101010 => 1101010101 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> 1010101100 => 1101010011 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> 1010110010 => 1101001101 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> 1010101100 => 1101010011 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1010111000 => 1101000111 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> 1011001010 => 1100110101 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 1011001100 => 1100110011 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> 1010110010 => 1101001101 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 1011001100 => 1100110011 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1010111000 => 1101000111 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1011100010 => 1100011101 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 1011001100 => 1100110011 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1010111000 => 1101000111 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 1011110000 => 1100001111 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 1100101010 => 0111010101 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> 1100101100 => 0111010011 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 1100110010 => 0111001101 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> 1100101100 => 0111010011 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 1100111000 => 0111000111 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> 1011001010 => 1100110101 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 1011001100 => 1100110011 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 1100110010 => 0111001101 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 1011001100 => 1100110011 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 1100111000 => 0111000111 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1011100010 => 1100011101 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 1011001100 => 1100110011 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 1100111000 => 0111000111 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 1011110000 => 1100001111 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1110001010 => 0011110101 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> 1110001100 => 0011110011 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 1100110010 => 0111001101 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> 1110001100 => 0011110011 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 1100111000 => 0111000111 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1011100010 => 1100011101 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> 1110001100 => 0011110011 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 1100111000 => 0111000111 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 1011110000 => 1100001111 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1111000010 => 0001111101 => 3 = 5 - 2
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> 1110001100 => 0011110011 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 1100111000 => 0111000111 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 1011110000 => 1100001111 => ? ∊ {4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,10} - 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1111100000 => 0000111111 => 1 = 3 - 2
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> 101010101010 => 110101010101 => ? ∊ {3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> 101010101100 => 110101010011 => ? ∊ {3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> 101010110010 => 110101001101 => ? ∊ {3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> 101010101100 => 110101010011 => ? ∊ {3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> 101010111000 => 110101000111 => ? ∊ {3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> 101011001010 => 110100110101 => ? ∊ {3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> 101011001100 => 110100110011 => ? ∊ {3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> 101010110010 => 110101001101 => ? ∊ {3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> 101011001100 => 110100110011 => ? ∊ {3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> 101010111000 => 110101000111 => ? ∊ {3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,12} - 2
Description
The number of changes of a binary word.
This is the number of indices $i$ such that $w_i \neq w_{i+1}$.
The following 1 statistic also match your data. Click on any of them to see the details.
St001877Number of indecomposable injective modules with projective dimension 2.
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