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Matching statistic: St000111
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
St000111: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[1,2] => 0
[2,1] => 2
[1,2,3] => 0
[1,3,2] => 3
[2,1,3] => 2
[2,3,1] => 3
[3,1,2] => 3
[3,2,1] => 5
[1,2,3,4] => 0
[1,2,4,3] => 4
[1,3,2,4] => 3
[1,3,4,2] => 4
[1,4,2,3] => 4
[1,4,3,2] => 7
[2,1,3,4] => 2
[2,1,4,3] => 6
[2,3,1,4] => 3
[2,3,4,1] => 4
[2,4,1,3] => 4
[2,4,3,1] => 7
[3,1,2,4] => 3
[3,1,4,2] => 7
[3,2,1,4] => 5
[3,2,4,1] => 7
[3,4,1,2] => 4
[3,4,2,1] => 6
[4,1,2,3] => 4
[4,1,3,2] => 7
[4,2,1,3] => 6
[4,2,3,1] => 7
[4,3,1,2] => 7
[4,3,2,1] => 9
[1,2,3,4,5] => 0
[1,2,3,5,4] => 5
[1,2,4,3,5] => 4
[1,2,4,5,3] => 5
[1,2,5,3,4] => 5
[1,2,5,4,3] => 9
[1,3,2,4,5] => 3
[1,3,2,5,4] => 8
[1,3,4,2,5] => 4
[1,3,4,5,2] => 5
[1,3,5,2,4] => 5
[1,3,5,4,2] => 9
[1,4,2,3,5] => 4
[1,4,2,5,3] => 9
[1,4,3,2,5] => 7
[1,4,3,5,2] => 9
[1,4,5,2,3] => 5
Description
The sum of the descent tops (or Genocchi descents) of a permutation.
This statistic is given by
$$\pi \mapsto \sum_{i\in\operatorname{Des}(\pi)} \pi_i.$$
Matching statistic: St000391
Mp00130: Permutations —descent tops⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
St000391: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
St000391: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => => [1] => 1 => 1 = 0 + 1
[1,2] => 0 => [2] => 10 => 1 = 0 + 1
[2,1] => 1 => [1,1] => 11 => 3 = 2 + 1
[1,2,3] => 00 => [3] => 100 => 1 = 0 + 1
[1,3,2] => 01 => [2,1] => 101 => 4 = 3 + 1
[2,1,3] => 10 => [1,2] => 110 => 3 = 2 + 1
[2,3,1] => 01 => [2,1] => 101 => 4 = 3 + 1
[3,1,2] => 01 => [2,1] => 101 => 4 = 3 + 1
[3,2,1] => 11 => [1,1,1] => 111 => 6 = 5 + 1
[1,2,3,4] => 000 => [4] => 1000 => 1 = 0 + 1
[1,2,4,3] => 001 => [3,1] => 1001 => 5 = 4 + 1
[1,3,2,4] => 010 => [2,2] => 1010 => 4 = 3 + 1
[1,3,4,2] => 001 => [3,1] => 1001 => 5 = 4 + 1
[1,4,2,3] => 001 => [3,1] => 1001 => 5 = 4 + 1
[1,4,3,2] => 011 => [2,1,1] => 1011 => 8 = 7 + 1
[2,1,3,4] => 100 => [1,3] => 1100 => 3 = 2 + 1
[2,1,4,3] => 101 => [1,2,1] => 1101 => 7 = 6 + 1
[2,3,1,4] => 010 => [2,2] => 1010 => 4 = 3 + 1
[2,3,4,1] => 001 => [3,1] => 1001 => 5 = 4 + 1
[2,4,1,3] => 001 => [3,1] => 1001 => 5 = 4 + 1
[2,4,3,1] => 011 => [2,1,1] => 1011 => 8 = 7 + 1
[3,1,2,4] => 010 => [2,2] => 1010 => 4 = 3 + 1
[3,1,4,2] => 011 => [2,1,1] => 1011 => 8 = 7 + 1
[3,2,1,4] => 110 => [1,1,2] => 1110 => 6 = 5 + 1
[3,2,4,1] => 011 => [2,1,1] => 1011 => 8 = 7 + 1
[3,4,1,2] => 001 => [3,1] => 1001 => 5 = 4 + 1
[3,4,2,1] => 101 => [1,2,1] => 1101 => 7 = 6 + 1
[4,1,2,3] => 001 => [3,1] => 1001 => 5 = 4 + 1
[4,1,3,2] => 011 => [2,1,1] => 1011 => 8 = 7 + 1
[4,2,1,3] => 101 => [1,2,1] => 1101 => 7 = 6 + 1
[4,2,3,1] => 011 => [2,1,1] => 1011 => 8 = 7 + 1
[4,3,1,2] => 011 => [2,1,1] => 1011 => 8 = 7 + 1
[4,3,2,1] => 111 => [1,1,1,1] => 1111 => 10 = 9 + 1
[1,2,3,4,5] => 0000 => [5] => 10000 => 1 = 0 + 1
[1,2,3,5,4] => 0001 => [4,1] => 10001 => 6 = 5 + 1
[1,2,4,3,5] => 0010 => [3,2] => 10010 => 5 = 4 + 1
[1,2,4,5,3] => 0001 => [4,1] => 10001 => 6 = 5 + 1
[1,2,5,3,4] => 0001 => [4,1] => 10001 => 6 = 5 + 1
[1,2,5,4,3] => 0011 => [3,1,1] => 10011 => 10 = 9 + 1
[1,3,2,4,5] => 0100 => [2,3] => 10100 => 4 = 3 + 1
[1,3,2,5,4] => 0101 => [2,2,1] => 10101 => 9 = 8 + 1
[1,3,4,2,5] => 0010 => [3,2] => 10010 => 5 = 4 + 1
[1,3,4,5,2] => 0001 => [4,1] => 10001 => 6 = 5 + 1
[1,3,5,2,4] => 0001 => [4,1] => 10001 => 6 = 5 + 1
[1,3,5,4,2] => 0011 => [3,1,1] => 10011 => 10 = 9 + 1
[1,4,2,3,5] => 0010 => [3,2] => 10010 => 5 = 4 + 1
[1,4,2,5,3] => 0011 => [3,1,1] => 10011 => 10 = 9 + 1
[1,4,3,2,5] => 0110 => [2,1,2] => 10110 => 8 = 7 + 1
[1,4,3,5,2] => 0011 => [3,1,1] => 10011 => 10 = 9 + 1
[1,4,5,2,3] => 0001 => [4,1] => 10001 => 6 = 5 + 1
Description
The sum of the positions of the ones in a binary word.
Matching statistic: St000471
St000471: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => ? = 0
[1,2] => 2
[2,1] => 0
[1,2,3] => 5
[1,3,2] => 3
[2,1,3] => 3
[2,3,1] => 3
[3,1,2] => 2
[3,2,1] => 0
[1,2,3,4] => 9
[1,2,4,3] => 6
[1,3,2,4] => 7
[1,3,4,2] => 7
[1,4,2,3] => 7
[1,4,3,2] => 4
[2,1,3,4] => 7
[2,1,4,3] => 4
[2,3,1,4] => 7
[2,3,4,1] => 7
[2,4,1,3] => 7
[2,4,3,1] => 4
[3,1,2,4] => 6
[3,1,4,2] => 4
[3,2,1,4] => 4
[3,2,4,1] => 4
[3,4,1,2] => 6
[3,4,2,1] => 4
[4,1,2,3] => 5
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 3
[4,3,1,2] => 2
[4,3,2,1] => 0
[1,2,3,4,5] => 14
[1,2,3,5,4] => 10
[1,2,4,3,5] => 11
[1,2,4,5,3] => 11
[1,2,5,3,4] => 11
[1,2,5,4,3] => 7
[1,3,2,4,5] => 12
[1,3,2,5,4] => 8
[1,3,4,2,5] => 12
[1,3,4,5,2] => 12
[1,3,5,2,4] => 12
[1,3,5,4,2] => 8
[1,4,2,3,5] => 12
[1,4,2,5,3] => 9
[1,4,3,2,5] => 9
[1,4,3,5,2] => 9
[1,4,5,2,3] => 12
[1,4,5,3,2] => 9
Description
The sum of the ascent tops of a permutation.
Matching statistic: St001879
(load all 33 compositions to match this statistic)
(load all 33 compositions to match this statistic)
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 58%
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 58%
Values
[1] => [1] => [1] => ([],1)
=> ? = 0
[1,2] => [1,2] => [2,1] => ([],2)
=> ? ∊ {0,2}
[2,1] => [2,1] => [1,2] => ([(0,1)],2)
=> ? ∊ {0,2}
[1,2,3] => [1,3,2] => [2,1,3] => ([(0,2),(1,2)],3)
=> ? ∊ {0,3,3,3,5}
[1,3,2] => [1,3,2] => [2,1,3] => ([(0,2),(1,2)],3)
=> ? ∊ {0,3,3,3,5}
[2,1,3] => [2,1,3] => [3,2,1] => ([],3)
=> ? ∊ {0,3,3,3,5}
[2,3,1] => [2,3,1] => [3,1,2] => ([(1,2)],3)
=> ? ∊ {0,3,3,3,5}
[3,1,2] => [3,1,2] => [1,3,2] => ([(0,1),(0,2)],3)
=> ? ∊ {0,3,3,3,5}
[3,2,1] => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[1,2,3,4] => [1,4,3,2] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[1,2,4,3] => [1,4,3,2] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[1,3,2,4] => [1,4,3,2] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[1,3,4,2] => [1,4,3,2] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[1,4,2,3] => [1,4,3,2] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[1,4,3,2] => [1,4,3,2] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[2,1,3,4] => [2,1,4,3] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[2,1,4,3] => [2,1,4,3] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[2,3,1,4] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[2,3,4,1] => [2,4,3,1] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[2,4,1,3] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[2,4,3,1] => [2,4,3,1] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[3,1,2,4] => [3,1,4,2] => [4,2,1,3] => ([(1,3),(2,3)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[3,1,4,2] => [3,1,4,2] => [4,2,1,3] => ([(1,3),(2,3)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[3,2,1,4] => [3,2,1,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[3,2,4,1] => [3,2,4,1] => [4,3,1,2] => ([(2,3)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[3,4,1,2] => [3,4,1,2] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[3,4,2,1] => [3,4,2,1] => [4,1,2,3] => ([(1,2),(2,3)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[4,1,2,3] => [4,1,3,2] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,1,3,2] => [4,1,3,2] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,2,1,3] => [4,2,1,3] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[4,2,3,1] => [4,2,3,1] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[4,3,1,2] => [4,3,1,2] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ? ∊ {0,2,3,3,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[4,3,2,1] => [4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,3,4,5] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,2,3,5,4] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,2,4,3,5] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,2,4,5,3] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,2,5,3,4] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,2,5,4,3] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,3,2,4,5] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,3,2,5,4] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,3,4,2,5] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,3,4,5,2] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,3,5,2,4] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,3,5,4,2] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,4,2,3,5] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,4,2,5,3] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,4,3,2,5] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,4,3,5,2] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,4,5,2,3] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,4,5,3,2] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,5,2,3,4] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,5,2,4,3] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,5,3,2,4] => [1,5,4,3,2] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[5,1,2,3,4] => [5,1,4,3,2] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[5,1,2,4,3] => [5,1,4,3,2] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[5,1,3,2,4] => [5,1,4,3,2] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[5,1,3,4,2] => [5,1,4,3,2] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[5,1,4,2,3] => [5,1,4,3,2] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[5,1,4,3,2] => [5,1,4,3,2] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[5,2,1,3,4] => [5,2,1,4,3] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,2,1,4,3] => [5,2,1,4,3] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,2,3,4,1] => [5,2,4,3,1] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[5,2,4,3,1] => [5,2,4,3,1] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[5,4,1,2,3] => [5,4,1,3,2] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[5,4,1,3,2] => [5,4,1,3,2] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[5,4,3,2,1] => [5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[6,1,2,3,4,5] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,2,3,5,4] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,2,4,3,5] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,2,4,5,3] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,2,5,3,4] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,2,5,4,3] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,3,2,4,5] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,3,2,5,4] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,3,4,2,5] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,3,4,5,2] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,3,5,2,4] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,3,5,4,2] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,4,2,3,5] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,4,2,5,3] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,4,3,2,5] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,4,3,5,2] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,4,5,2,3] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,4,5,3,2] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,5,2,3,4] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,5,2,4,3] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,5,3,2,4] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,5,3,4,2] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,5,4,2,3] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,1,5,4,3,2] => [6,1,5,4,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,2,1,3,4,5] => [6,2,1,5,4,3] => [1,4,3,2,5,6] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> 10
[6,2,1,3,5,4] => [6,2,1,5,4,3] => [1,4,3,2,5,6] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> 10
[6,2,1,4,3,5] => [6,2,1,5,4,3] => [1,4,3,2,5,6] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> 10
[6,2,1,4,5,3] => [6,2,1,5,4,3] => [1,4,3,2,5,6] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> 10
[6,2,1,5,3,4] => [6,2,1,5,4,3] => [1,4,3,2,5,6] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> 10
[6,2,1,5,4,3] => [6,2,1,5,4,3] => [1,4,3,2,5,6] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> 10
[6,2,3,1,4,5] => [6,2,5,1,4,3] => [1,4,2,5,3,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 7
[6,2,3,1,5,4] => [6,2,5,1,4,3] => [1,4,2,5,3,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 7
[6,2,3,4,5,1] => [6,2,5,4,3,1] => [1,4,2,3,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> 7
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Matching statistic: St001232
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 47%
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 47%
Values
[1] => [1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1 = 0 + 1
[1,2] => [1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,1,0,0,1,0]
=> 1 = 0 + 1
[2,1] => [1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? = 2 + 1
[1,2,3] => [1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> 1 = 0 + 1
[1,3,2] => [1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> 3 = 2 + 1
[2,1,3] => [1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? ∊ {3,3,3,5} + 1
[2,3,1] => [1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> ? ∊ {3,3,3,5} + 1
[3,1,2] => [1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {3,3,3,5} + 1
[3,2,1] => [1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {3,3,3,5} + 1
[1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1 = 0 + 1
[1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4 = 3 + 1
[1,3,2,4] => [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]
=> 5 = 4 + 1
[1,3,4,2] => [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]
=> 3 = 2 + 1
[1,4,2,3] => [1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[1,4,3,2] => [1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[2,1,3,4] => [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[2,1,4,3] => [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[2,4,1,3] => [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]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[2,4,3,1] => [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]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[3,1,2,4] => [1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[3,1,4,2] => [1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[3,2,1,4] => [1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[3,2,4,1] => [1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[3,4,1,2] => [1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[3,4,2,1] => [1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[4,1,2,3] => [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]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[4,1,3,2] => [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]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[4,2,1,3] => [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]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[4,2,3,1] => [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]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[4,3,1,2] => [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]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[4,3,2,1] => [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]
=> ? ∊ {3,3,4,4,4,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9} + 1
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1 = 0 + 1
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 4 + 1
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> 7 = 6 + 1
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> 4 = 3 + 1
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> 7 = 6 + 1
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0,1,0]
=> 5 = 4 + 1
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,1,0,0,1,0]
=> 3 = 2 + 1
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 4 + 1
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 4 + 1
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,4,5,2,3] => [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]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,4,5,3,2] => [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]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> ? ∊ {3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14} + 1
[1,2,3,4,5,6] => [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]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> 1 = 0 + 1
[1,2,3,4,6,5] => [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]
=> [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> 6 = 5 + 1
[1,2,3,5,4,6] => [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]
=> [1,1,0,1,1,1,1,0,0,0,0,0,1,0]
=> 9 = 8 + 1
[1,2,3,5,6,4] => [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]
=> [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 4 + 1
[1,2,4,3,5,6] => [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]
=> [1,1,1,0,1,1,1,0,0,0,0,0,1,0]
=> 10 = 9 + 1
[1,2,4,5,3,6] => [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]
=> [1,1,1,0,0,1,1,1,0,0,0,0,1,0]
=> 7 = 6 + 1
[1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=> 4 = 3 + 1
[1,2,4,6,3,5] => [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]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 5 + 1
[1,2,4,6,5,3] => [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]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 5 + 1
[1,3,2,4,5,6] => [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]
=> [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=> 9 = 8 + 1
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
=> 7 = 6 + 1
[1,3,4,5,2,6] => [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]
=> [1,1,1,1,0,0,0,1,1,0,0,0,1,0]
=> 5 = 4 + 1
[1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> 3 = 2 + 1
[1,3,4,6,2,5] => [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]
=> [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> 6 = 5 + 1
[1,3,4,6,5,2] => [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]
=> [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> 6 = 5 + 1
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0,1,0]
=> 8 = 7 + 1
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0,1,0]
=> 7 = 6 + 1
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0,1,0]
=> 8 = 7 + 1
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0,1,0]
=> 7 = 6 + 1
[1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 4 + 1
[1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 4 + 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001880
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 21%
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 21%
Values
[1] => [1]
=> [[1],[]]
=> ([],1)
=> ? = 0
[1,2] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? ∊ {0,2}
[2,1] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? ∊ {0,2}
[1,2,3] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,3,2] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? ∊ {0,2,3,5}
[2,1,3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? ∊ {0,2,3,5}
[2,3,1] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? ∊ {0,2,3,5}
[3,1,2] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? ∊ {0,2,3,5}
[3,2,1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,2,3,4] => [1,1,1,1]
=> [[1,1,1,1],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,2,4,3] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[1,3,2,4] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[1,3,4,2] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[1,4,2,3] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[1,4,3,2] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[2,1,3,4] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[2,1,4,3] => [2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[2,3,1,4] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[2,3,4,1] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[2,4,1,3] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[2,4,3,1] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[3,1,2,4] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[3,1,4,2] => [2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[3,2,1,4] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[3,2,4,1] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[3,4,1,2] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[3,4,2,1] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[4,1,2,3] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[4,1,3,2] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[4,2,1,3] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[4,2,3,1] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[4,3,1,2] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,2,3,3,3,4,4,4,5,6,6,6,7,7,7,7,7,7,7,9}
[4,3,2,1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,2,3,4,5] => [1,1,1,1,1]
=> [[1,1,1,1,1],[]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,2,3,5,4] => [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,2,4,3,5] => [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,2,4,5,3] => [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,2,5,3,4] => [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,2,5,4,3] => [3,1,1]
=> [[3,1,1],[]]
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,3,2,4,5] => [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,3,2,5,4] => [2,2,1]
=> [[2,2,1],[]]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,3,4,2,5] => [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,3,4,5,2] => [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,3,5,2,4] => [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,3,5,4,2] => [3,1,1]
=> [[3,1,1],[]]
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,4,2,3,5] => [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,4,2,5,3] => [2,2,1]
=> [[2,2,1],[]]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,4,3,2,5] => [3,1,1]
=> [[3,1,1],[]]
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,4,3,5,2] => [3,1,1]
=> [[3,1,1],[]]
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,4,5,2,3] => [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,4,5,3,2] => [3,1,1]
=> [[3,1,1],[]]
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,5,2,3,4] => [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,5,2,4,3] => [3,1,1]
=> [[3,1,1],[]]
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,5,3,2,4] => [3,1,1]
=> [[3,1,1],[]]
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,5,3,4,2] => [3,1,1]
=> [[3,1,1],[]]
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,5,4,2,3] => [3,1,1]
=> [[3,1,1],[]]
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[1,5,4,3,2] => [4,1]
=> [[4,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,2,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,14}
[5,4,3,2,1] => [5]
=> [[5],[]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,2,3,4,5,6] => [1,1,1,1,1,1]
=> [[1,1,1,1,1,1],[]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[2,1,4,3,6,5] => [2,2,2]
=> [[2,2,2],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[2,1,5,3,6,4] => [2,2,2]
=> [[2,2,2],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[3,1,4,2,6,5] => [2,2,2]
=> [[2,2,2],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[3,1,5,2,6,4] => [2,2,2]
=> [[2,2,2],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[3,2,1,6,5,4] => [3,3]
=> [[3,3],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[4,1,5,2,6,3] => [2,2,2]
=> [[2,2,2],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[4,2,1,6,5,3] => [3,3]
=> [[3,3],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[4,3,1,6,5,2] => [3,3]
=> [[3,3],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[5,2,1,6,4,3] => [3,3]
=> [[3,3],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[5,3,1,6,4,2] => [3,3]
=> [[3,3],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[6,5,4,3,2,1] => [6]
=> [[6],[]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
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