searching the database
Your data matches 5 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000229
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
St000229: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
=> 1
{{1,2}}
=> 2
{{1},{2}}
=> 2
{{1,2,3}}
=> 3
{{1,2},{3}}
=> 3
{{1,3},{2}}
=> 4
{{1},{2,3}}
=> 3
{{1},{2},{3}}
=> 3
{{1,2,3,4}}
=> 4
{{1,2,3},{4}}
=> 4
{{1,2,4},{3}}
=> 5
{{1,2},{3,4}}
=> 4
{{1,2},{3},{4}}
=> 4
{{1,3,4},{2}}
=> 5
{{1,3},{2,4}}
=> 6
{{1,3},{2},{4}}
=> 5
{{1,4},{2,3}}
=> 6
{{1},{2,3,4}}
=> 4
{{1},{2,3},{4}}
=> 4
{{1,4},{2},{3}}
=> 6
{{1},{2,4},{3}}
=> 5
{{1},{2},{3,4}}
=> 4
{{1},{2},{3},{4}}
=> 4
{{1,2,3,4,5}}
=> 5
{{1,2,3,4},{5}}
=> 5
{{1,2,3,5},{4}}
=> 6
{{1,2,3},{4,5}}
=> 5
{{1,2,3},{4},{5}}
=> 5
{{1,2,4,5},{3}}
=> 6
{{1,2,4},{3,5}}
=> 7
{{1,2,4},{3},{5}}
=> 6
{{1,2,5},{3,4}}
=> 7
{{1,2},{3,4,5}}
=> 5
{{1,2},{3,4},{5}}
=> 5
{{1,2,5},{3},{4}}
=> 7
{{1,2},{3,5},{4}}
=> 6
{{1,2},{3},{4,5}}
=> 5
{{1,2},{3},{4},{5}}
=> 5
{{1,3,4,5},{2}}
=> 6
{{1,3,4},{2,5}}
=> 8
{{1,3,4},{2},{5}}
=> 6
{{1,3,5},{2,4}}
=> 8
{{1,3},{2,4,5}}
=> 7
{{1,3},{2,4},{5}}
=> 7
{{1,3,5},{2},{4}}
=> 7
{{1,3},{2,5},{4}}
=> 8
{{1,3},{2},{4,5}}
=> 6
{{1,3},{2},{4},{5}}
=> 6
{{1,4,5},{2,3}}
=> 7
{{1,4},{2,3,5}}
=> 8
Description
Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition.
This is, for a set partition $P = \{B_1,\ldots,B_k\}$ of $\{1,\ldots,n\}$, the statistic is
$$d(P) = \sum_i \big(\operatorname{max}(B_i)-\operatorname{min}(B_i)+1\big).$$
This statistic is called ''dimension index'' in [2]
Matching statistic: St001232
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 67%
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 67%
Values
{{1}}
=> [1] => [1] => [1,0]
=> 0 = 1 - 1
{{1,2}}
=> [2,1] => [1,2] => [1,0,1,0]
=> 1 = 2 - 1
{{1},{2}}
=> [1,2] => [1,2] => [1,0,1,0]
=> 1 = 2 - 1
{{1,2,3}}
=> [2,3,1] => [1,2,3] => [1,0,1,0,1,0]
=> ? ∊ {3,3,3,4} - 1
{{1,2},{3}}
=> [2,1,3] => [1,2,3] => [1,0,1,0,1,0]
=> ? ∊ {3,3,3,4} - 1
{{1,3},{2}}
=> [3,2,1] => [1,3,2] => [1,0,1,1,0,0]
=> 2 = 3 - 1
{{1},{2,3}}
=> [1,3,2] => [1,2,3] => [1,0,1,0,1,0]
=> ? ∊ {3,3,3,4} - 1
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
=> ? ∊ {3,3,3,4} - 1
{{1,2,3,4}}
=> [2,3,4,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> ? ∊ {4,4,4,4,5,5,5,5,6,6,6} - 1
{{1,2,3},{4}}
=> [2,3,1,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> ? ∊ {4,4,4,4,5,5,5,5,6,6,6} - 1
{{1,2,4},{3}}
=> [2,4,3,1] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> ? ∊ {4,4,4,4,5,5,5,5,6,6,6} - 1
{{1,2},{3,4}}
=> [2,1,4,3] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> ? ∊ {4,4,4,4,5,5,5,5,6,6,6} - 1
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> ? ∊ {4,4,4,4,5,5,5,5,6,6,6} - 1
{{1,3,4},{2}}
=> [3,2,4,1] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
=> ? ∊ {4,4,4,4,5,5,5,5,6,6,6} - 1
{{1,3},{2,4}}
=> [3,4,1,2] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> 3 = 4 - 1
{{1,3},{2},{4}}
=> [3,2,1,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> 3 = 4 - 1
{{1,4},{2,3}}
=> [4,3,2,1] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
=> 3 = 4 - 1
{{1},{2,3,4}}
=> [1,3,4,2] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> ? ∊ {4,4,4,4,5,5,5,5,6,6,6} - 1
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> ? ∊ {4,4,4,4,5,5,5,5,6,6,6} - 1
{{1,4},{2},{3}}
=> [4,2,3,1] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
=> 3 = 4 - 1
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> ? ∊ {4,4,4,4,5,5,5,5,6,6,6} - 1
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> ? ∊ {4,4,4,4,5,5,5,5,6,6,6} - 1
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> ? ∊ {4,4,4,4,5,5,5,5,6,6,6} - 1
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> 4 = 5 - 1
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
=> 4 = 5 - 1
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
=> 4 = 5 - 1
{{1,5},{2,3,4}}
=> [5,3,4,2,1] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
=> 4 = 5 - 1
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
=> 4 = 5 - 1
{{1},{2,3,5},{4}}
=> [1,3,5,4,2] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1},{2,3},{4,5}}
=> [1,3,2,5,4] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,4,5},{2},{3}}
=> [4,2,3,5,1] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,4},{2,5},{3}}
=> [4,5,3,1,2] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
=> 5 = 6 - 1
{{1,4},{2},{3,5}}
=> [4,2,5,1,3] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
=> 4 = 5 - 1
{{1,4},{2},{3},{5}}
=> [4,2,3,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
=> 4 = 5 - 1
{{1,5},{2,4},{3}}
=> [5,4,3,2,1] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
=> 4 = 5 - 1
{{1},{2,4,5},{3}}
=> [1,4,3,5,2] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1},{2,4},{3,5}}
=> [1,4,5,2,3] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1},{2,4},{3},{5}}
=> [1,4,3,2,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,5},{2},{3,4}}
=> [5,2,4,3,1] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
=> 4 = 5 - 1
{{1},{2,5},{3,4}}
=> [1,5,4,3,2] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
=> ? ∊ {5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9} - 1
{{1,5},{2},{3},{4}}
=> [5,2,3,4,1] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
=> 4 = 5 - 1
{{1,3},{2,5},{4,6}}
=> [3,5,1,6,2,4] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 6 - 1
{{1,3},{2,5},{4},{6}}
=> [3,5,1,4,2,6] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 6 - 1
{{1,3},{2,6},{4,5}}
=> [3,6,1,5,4,2] => [1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> 5 = 6 - 1
{{1,3},{2,6},{4},{5}}
=> [3,6,1,4,5,2] => [1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> 5 = 6 - 1
{{1,4},{2,3,6},{5}}
=> [4,3,6,1,5,2] => [1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5 = 6 - 1
{{1,5},{2,3,4,6}}
=> [5,3,4,6,1,2] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
{{1,5},{2,3,4},{6}}
=> [5,3,4,2,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
{{1,6},{2,3,4,5}}
=> [6,3,4,5,2,1] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
{{1,6},{2,3,4},{5}}
=> [6,3,4,2,5,1] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
{{1,5},{2,3,6},{4}}
=> [5,3,6,4,1,2] => [1,5,2,3,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0]
=> 6 = 7 - 1
{{1,5},{2,3},{4,6}}
=> [5,3,2,6,1,4] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
{{1,5},{2,3},{4},{6}}
=> [5,3,2,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
{{1,6},{2,3,5},{4}}
=> [6,3,5,4,2,1] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
{{1,6},{2,3},{4,5}}
=> [6,3,2,5,4,1] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
{{1,6},{2,3},{4},{5}}
=> [6,3,2,4,5,1] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
{{1,4},{2,6},{3,5}}
=> [4,6,5,1,3,2] => [1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> 7 = 8 - 1
{{1,4},{2,6},{3},{5}}
=> [4,6,3,1,5,2] => [1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> 7 = 8 - 1
{{1,4},{2},{3,6},{5}}
=> [4,2,6,1,5,3] => [1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5 = 6 - 1
{{1,5},{2,4,6},{3}}
=> [5,4,3,6,1,2] => [1,5,2,4,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0]
=> 6 = 7 - 1
{{1,5},{2,4},{3,6}}
=> [5,4,6,2,1,3] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
{{1,5},{2,4},{3},{6}}
=> [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
{{1,6},{2,4,5},{3}}
=> [6,4,3,5,2,1] => [1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
{{1,6},{2,4},{3,5}}
=> [6,4,5,2,3,1] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
{{1,6},{2,4},{3},{5}}
=> [6,4,3,2,5,1] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
{{1,5},{2,6},{3,4}}
=> [5,6,4,3,1,2] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0]
=> 7 = 8 - 1
{{1,5},{2},{3,4,6}}
=> [5,2,4,6,1,3] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
{{1,5},{2},{3,4},{6}}
=> [5,2,4,3,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5 = 6 - 1
{{1,6},{2,5},{3,4}}
=> [6,5,4,3,2,1] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
{{1,6},{2},{3,4,5}}
=> [6,2,4,5,3,1] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
{{1,6},{2},{3,4},{5}}
=> [6,2,4,3,5,1] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5 = 6 - 1
{{1,5},{2,6},{3},{4}}
=> [5,6,3,4,1,2] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0]
=> 7 = 8 - 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001880
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 33%
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 33%
Values
{{1}}
=> [1] => [.,.]
=> ([],1)
=> ? = 1
{{1,2}}
=> [2,1] => [[.,.],.]
=> ([(0,1)],2)
=> ? ∊ {2,2}
{{1},{2}}
=> [1,2] => [.,[.,.]]
=> ([(0,1)],2)
=> ? ∊ {2,2}
{{1,2,3}}
=> [2,3,1] => [[.,[.,.]],.]
=> ([(0,2),(2,1)],3)
=> 3
{{1,2},{3}}
=> [2,1,3] => [[.,.],[.,.]]
=> ([(0,2),(1,2)],3)
=> ? = 4
{{1,3},{2}}
=> [3,2,1] => [[[.,.],.],.]
=> ([(0,2),(2,1)],3)
=> 3
{{1},{2,3}}
=> [1,3,2] => [.,[[.,.],.]]
=> ([(0,2),(2,1)],3)
=> 3
{{1},{2},{3}}
=> [1,2,3] => [.,[.,[.,.]]]
=> ([(0,2),(2,1)],3)
=> 3
{{1,2,3,4}}
=> [2,3,4,1] => [[.,[.,[.,.]]],.]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
{{1,2,3},{4}}
=> [2,3,1,4] => [[.,[.,.]],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {4,5,5,5,5,6,6,6}
{{1,2,4},{3}}
=> [2,4,3,1] => [[.,[[.,.],.]],.]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
{{1,2},{3,4}}
=> [2,1,4,3] => [[.,.],[[.,.],.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {4,5,5,5,5,6,6,6}
{{1,2},{3},{4}}
=> [2,1,3,4] => [[.,.],[.,[.,.]]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {4,5,5,5,5,6,6,6}
{{1,3,4},{2}}
=> [3,2,4,1] => [[[.,.],[.,.]],.]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,5,5,5,5,6,6,6}
{{1,3},{2,4}}
=> [3,4,1,2] => [[.,[.,.]],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {4,5,5,5,5,6,6,6}
{{1,3},{2},{4}}
=> [3,2,1,4] => [[[.,.],.],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {4,5,5,5,5,6,6,6}
{{1,4},{2,3}}
=> [4,3,2,1] => [[[[.,.],.],.],.]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
{{1},{2,3,4}}
=> [1,3,4,2] => [.,[[.,[.,.]],.]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
{{1},{2,3},{4}}
=> [1,3,2,4] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,5,5,5,5,6,6,6}
{{1,4},{2},{3}}
=> [4,2,3,1] => [[[.,.],[.,.]],.]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,5,5,5,5,6,6,6}
{{1},{2,4},{3}}
=> [1,4,3,2] => [.,[[[.,.],.],.]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
{{1},{2},{3,4}}
=> [1,2,4,3] => [.,[.,[[.,.],.]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
{{1},{2},{3},{4}}
=> [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [[.,[.,[[.,.],.]]],.]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [[.,[.,.]],[[.,.],.]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [[.,[[.,.],.]],[.,.]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [[.,[[[.,.],.],.]],.]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [[.,.],[[.,[.,.]],.]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [[.,[[.,.],[.,.]]],.]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [[[.,.],[.,[.,.]]],.]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [[.,[[.,.],.]],[.,.]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [[[.,.],[.,.]],[.,.]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [[[.,[.,[.,.]]],.],.]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [[.,[.,.]],[[.,.],.]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [[[.,.],[[.,.],.]],.]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [[.,[.,.]],[[.,.],.]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [[[[.,.],.],[.,.]],.]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [[[.,.],[.,.]],[.,.]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,5},{2,3,4}}
=> [5,3,4,2,1] => [[[[.,.],[.,.]],.],.]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
{{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [[[[.,.],.],[.,.]],.]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,3,5},{4}}
=> [1,3,5,4,2] => [.,[[.,[[.,.],.]],.]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
{{1},{2,3},{4,5}}
=> [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4,5},{2},{3}}
=> [4,2,3,5,1] => [[[.,.],[.,[.,.]]],.]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4},{2,5},{3}}
=> [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4},{2},{3,5}}
=> [4,2,5,1,3] => [[[.,.],[.,.]],[.,.]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4},{2},{3},{5}}
=> [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,5},{2,4},{3}}
=> [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
{{1},{2,4,5},{3}}
=> [1,4,3,5,2] => [.,[[[.,.],[.,.]],.]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,4},{3,5}}
=> [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,4},{3},{5}}
=> [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,5},{2},{3,4}}
=> [5,2,4,3,1] => [[[.,.],[[.,.],.]],.]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,5},{3,4}}
=> [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
{{1},{2},{3,4,5}}
=> [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
{{1},{2},{3,4},{5}}
=> [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2},{3,5},{4}}
=> [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
{{1},{2},{3},{4,5}}
=> [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
{{1},{2},{3},{4},{5}}
=> [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
{{1,2,3,4,5,6}}
=> [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1,2,3,4,6},{5}}
=> [2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1,2,3,6},{4,5}}
=> [2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1,2,4,6},{3,5}}
=> [2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1,2,6},{3,5},{4}}
=> [2,6,5,4,3,1] => [[.,[[[[.,.],.],.],.]],.]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1,3,6},{2,4,5}}
=> [3,4,6,5,2,1] => [[[.,[.,[[.,.],.]]],.],.]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1,3,6},{2,5},{4}}
=> [3,5,6,4,2,1] => [[[.,[[.,[.,.]],.]],.],.]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1},{2,3,4,5,6}}
=> [1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1},{2,3,4,6},{5}}
=> [1,3,4,6,5,2] => [.,[[.,[.,[[.,.],.]]],.]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1},{2,3,6},{4,5}}
=> [1,3,6,5,4,2] => [.,[[.,[[[.,.],.],.]],.]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1},{2,4,6},{3,5}}
=> [1,4,5,6,3,2] => [.,[[[.,[.,[.,.]]],.],.]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1,6},{2,5},{3,4}}
=> [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1},{2},{3,4,5,6}}
=> [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1},{2},{3,4,6},{5}}
=> [1,2,4,6,5,3] => [.,[.,[[.,[[.,.],.]],.]]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1},{2,6},{3,5},{4}}
=> [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1},{2},{3,6},{4,5}}
=> [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1},{2},{3},{4,5,6}}
=> [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1},{2},{3},{4,6},{5}}
=> [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1},{2},{3},{4},{5,6}}
=> [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1},{2},{3},{4},{5},{6}}
=> [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
=> ([(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.
Matching statistic: St001894
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
Mp00167: Signed permutations —inverse Kreweras complement⟶ Signed permutations
St001894: Signed permutations ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 58%
Mp00170: Permutations —to signed permutation⟶ Signed permutations
Mp00167: Signed permutations —inverse Kreweras complement⟶ Signed permutations
St001894: Signed permutations ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 58%
Values
{{1}}
=> [1] => [1] => [-1] => 1
{{1,2}}
=> [2,1] => [2,1] => [1,-2] => 2
{{1},{2}}
=> [1,2] => [1,2] => [2,-1] => 2
{{1,2,3}}
=> [2,3,1] => [2,3,1] => [1,2,-3] => 3
{{1,2},{3}}
=> [2,1,3] => [2,1,3] => [1,3,-2] => 3
{{1,3},{2}}
=> [3,2,1] => [3,2,1] => [2,1,-3] => 4
{{1},{2,3}}
=> [1,3,2] => [1,3,2] => [3,2,-1] => 3
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => [2,3,-1] => 3
{{1,2,3,4}}
=> [2,3,4,1] => [2,3,4,1] => [1,2,3,-4] => 4
{{1,2,3},{4}}
=> [2,3,1,4] => [2,3,1,4] => [1,2,4,-3] => 4
{{1,2,4},{3}}
=> [2,4,3,1] => [2,4,3,1] => [1,3,2,-4] => 5
{{1,2},{3,4}}
=> [2,1,4,3] => [2,1,4,3] => [1,4,3,-2] => 4
{{1,2},{3},{4}}
=> [2,1,3,4] => [2,1,3,4] => [1,3,4,-2] => 4
{{1,3,4},{2}}
=> [3,2,4,1] => [3,2,4,1] => [2,1,3,-4] => 5
{{1,3},{2,4}}
=> [3,4,1,2] => [3,4,1,2] => [4,1,2,-3] => 6
{{1,3},{2},{4}}
=> [3,2,1,4] => [3,2,1,4] => [2,1,4,-3] => 5
{{1,4},{2,3}}
=> [4,3,2,1] => [4,3,2,1] => [3,2,1,-4] => 6
{{1},{2,3,4}}
=> [1,3,4,2] => [1,3,4,2] => [4,2,3,-1] => 4
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,3,2,4] => [3,2,4,-1] => 4
{{1,4},{2},{3}}
=> [4,2,3,1] => [4,2,3,1] => [2,3,1,-4] => 6
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,4,3,2] => [4,3,2,-1] => 5
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,4,3] => [2,4,3,-1] => 4
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => [2,3,4,-1] => 4
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [2,3,4,5,1] => [1,2,3,4,-5] => 5
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [2,3,4,1,5] => [1,2,3,5,-4] => 5
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [2,3,5,4,1] => [1,2,4,3,-5] => 6
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [2,3,1,5,4] => [1,2,5,4,-3] => 5
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [2,3,1,4,5] => [1,2,4,5,-3] => 5
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [2,4,3,5,1] => [1,3,2,4,-5] => 6
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [2,4,5,1,3] => [1,5,2,3,-4] => 7
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [2,4,3,1,5] => [1,3,2,5,-4] => 6
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [2,5,4,3,1] => [1,4,3,2,-5] => 7
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [2,1,4,5,3] => [1,5,3,4,-2] => 5
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [2,1,4,3,5] => [1,4,3,5,-2] => 5
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [2,5,3,4,1] => [1,3,4,2,-5] => 7
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [2,1,5,4,3] => [1,5,4,3,-2] => 6
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [2,1,3,5,4] => [1,3,5,4,-2] => 5
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [2,1,3,4,5] => [1,3,4,5,-2] => 5
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [3,2,4,5,1] => [2,1,3,4,-5] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [3,5,4,1,2] => [5,1,3,2,-4] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [3,2,4,1,5] => [2,1,3,5,-4] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [3,4,5,2,1] => [4,1,2,3,-5] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [3,4,1,5,2] => [5,1,2,4,-3] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [3,4,1,2,5] => [4,1,2,5,-3] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [3,2,5,4,1] => [2,1,4,3,-5] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [3,5,1,4,2] => [5,1,4,2,-3] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [3,2,1,5,4] => [2,1,5,4,-3] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [3,2,1,4,5] => [2,1,4,5,-3] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [4,3,2,5,1] => [3,2,1,4,-5] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [4,3,5,1,2] => [5,2,1,3,-4] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [4,3,2,1,5] => [3,2,1,5,-4] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,5},{2,3,4}}
=> [5,3,4,2,1] => [5,3,4,2,1] => [4,2,3,1,-5] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,3,4,5,2] => [5,2,3,4,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [1,3,4,2,5] => [4,2,3,5,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [5,3,2,4,1] => [3,2,4,1,-5] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,3,5},{4}}
=> [1,3,5,4,2] => [1,3,5,4,2] => [5,2,4,3,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,3},{4,5}}
=> [1,3,2,5,4] => [1,3,2,5,4] => [3,2,5,4,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => [1,3,2,4,5] => [3,2,4,5,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4,5},{2},{3}}
=> [4,2,3,5,1] => [4,2,3,5,1] => [2,3,1,4,-5] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4},{2,5},{3}}
=> [4,5,3,1,2] => [4,5,3,1,2] => [5,3,1,2,-4] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4},{2},{3,5}}
=> [4,2,5,1,3] => [4,2,5,1,3] => [2,5,1,3,-4] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4},{2},{3},{5}}
=> [4,2,3,1,5] => [4,2,3,1,5] => [2,3,1,5,-4] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,5},{2,4},{3}}
=> [5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1,-5] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,4,5},{3}}
=> [1,4,3,5,2] => [1,4,3,5,2] => [5,3,2,4,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,4},{3,5}}
=> [1,4,5,2,3] => [1,4,5,2,3] => [4,5,2,3,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,4},{3},{5}}
=> [1,4,3,2,5] => [1,4,3,2,5] => [4,3,2,5,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,5},{2},{3,4}}
=> [5,2,4,3,1] => [5,2,4,3,1] => [2,4,3,1,-5] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,5},{3,4}}
=> [1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,2,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2},{3,4,5}}
=> [1,2,4,5,3] => [1,2,4,5,3] => [2,5,3,4,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2},{3,4},{5}}
=> [1,2,4,3,5] => [1,2,4,3,5] => [2,4,3,5,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,5},{2},{3},{4}}
=> [5,2,3,4,1] => [5,2,3,4,1] => [2,3,4,1,-5] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,5},{3},{4}}
=> [1,5,3,4,2] => [1,5,3,4,2] => [5,3,4,2,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2},{3,5},{4}}
=> [1,2,5,4,3] => [1,2,5,4,3] => [2,5,4,3,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2},{3},{4,5}}
=> [1,2,3,5,4] => [1,2,3,5,4] => [2,3,5,4,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2},{3},{4},{5}}
=> [1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,-1] => ? ∊ {5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,3,4,5,6}}
=> [2,3,4,5,6,1] => [2,3,4,5,6,1] => [1,2,3,4,5,-6] => ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12}
{{1,2,3,4,5},{6}}
=> [2,3,4,5,1,6] => [2,3,4,5,1,6] => [1,2,3,4,6,-5] => ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12}
{{1,2,3,4,6},{5}}
=> [2,3,4,6,5,1] => [2,3,4,6,5,1] => [1,2,3,5,4,-6] => ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12}
{{1,2,3,4},{5,6}}
=> [2,3,4,1,6,5] => [2,3,4,1,6,5] => [1,2,3,6,5,-4] => ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12}
{{1,2,3,4},{5},{6}}
=> [2,3,4,1,5,6] => [2,3,4,1,5,6] => [1,2,3,5,6,-4] => ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12}
{{1,2,3,5,6},{4}}
=> [2,3,5,4,6,1] => [2,3,5,4,6,1] => [1,2,4,3,5,-6] => ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12}
{{1,2,3,5},{4,6}}
=> [2,3,5,6,1,4] => [2,3,5,6,1,4] => [1,2,6,3,4,-5] => ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12}
{{1,2,3,5},{4},{6}}
=> [2,3,5,4,1,6] => [2,3,5,4,1,6] => [1,2,4,3,6,-5] => ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12}
{{1,2,3,6},{4,5}}
=> [2,3,6,5,4,1] => [2,3,6,5,4,1] => [1,2,5,4,3,-6] => ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12}
{{1,2,3},{4,5,6}}
=> [2,3,1,5,6,4] => [2,3,1,5,6,4] => [1,2,6,4,5,-3] => ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12}
{{1,2,3},{4,5},{6}}
=> [2,3,1,5,4,6] => [2,3,1,5,4,6] => [1,2,5,4,6,-3] => ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12}
{{1,2,3,6},{4},{5}}
=> [2,3,6,4,5,1] => [2,3,6,4,5,1] => [1,2,4,5,3,-6] => ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12}
{{1,2,3},{4,6},{5}}
=> [2,3,1,6,5,4] => [2,3,1,6,5,4] => [1,2,6,5,4,-3] => ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12}
Description
The depth of a signed permutation.
The depth of a positive root is its rank in the root poset. The depth of an element of a Coxeter group is the minimal sum of depths for any representation as product of reflections.
Matching statistic: St001645
(load all 9 compositions to match this statistic)
(load all 9 compositions to match this statistic)
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 50%
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 50%
Values
{{1}}
=> [1] => [1] => ([],1)
=> 1
{{1,2}}
=> [2,1] => [2,1] => ([(0,1)],2)
=> 2
{{1},{2}}
=> [1,2] => [1,2] => ([],2)
=> ? = 2
{{1,2,3}}
=> [2,3,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
{{1,2},{3}}
=> [2,1,3] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {3,3,3}
{{1,3},{2}}
=> [3,2,1] => [2,3,1] => ([(0,2),(1,2)],3)
=> 4
{{1},{2,3}}
=> [1,3,2] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {3,3,3}
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {3,3,3}
{{1,2,3,4}}
=> [2,3,4,1] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,5,5,5,5,6,6,6}
{{1,2,3},{4}}
=> [2,3,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,5,5,5,5,6,6,6}
{{1,2,4},{3}}
=> [2,4,3,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,5,5,5,5,6,6,6}
{{1,2},{3,4}}
=> [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,5,5,5,5,6,6,6}
{{1,2},{3},{4}}
=> [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,5,5,5,5,6,6,6}
{{1,3,4},{2}}
=> [3,2,4,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
{{1,3},{2,4}}
=> [3,4,1,2] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,5,5,5,5,6,6,6}
{{1,3},{2},{4}}
=> [3,2,1,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,5,5,5,5,6,6,6}
{{1,4},{2,3}}
=> [4,3,2,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,5,5,5,5,6,6,6}
{{1},{2,3,4}}
=> [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,5,5,5,5,6,6,6}
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,5,5,5,5,6,6,6}
{{1,4},{2},{3}}
=> [4,2,3,1] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,5,5,5,5,6,6,6}
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,5,5,5,5,6,6,6}
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,5,5,5,5,6,6,6}
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {4,4,4,4,4,4,4,5,5,5,5,6,6,6}
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [4,2,3,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [2,1,4,3,5] => ([(1,4),(2,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [4,2,5,3,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [2,1,3,5,4] => ([(1,4),(2,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [2,1,3,4,5] => ([(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [4,1,3,5,2] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [2,5,3,4,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [4,1,3,2,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 5
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [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
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,5},{2,3,4}}
=> [5,3,4,2,1] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,3,5},{4}}
=> [1,3,5,4,2] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,3},{4,5}}
=> [1,3,2,5,4] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => [1,3,2,4,5] => ([(3,4)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9}
{{1,4,5},{2},{3}}
=> [4,2,3,5,1] => [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
{{1,5},{2},{3},{4}}
=> [5,2,3,4,1] => [4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 5
{{1,3,4},{2,5,6}}
=> [3,5,4,1,6,2] => [6,4,3,5,1,2] => ([(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
{{1,3,5,6},{2,4}}
=> [3,4,5,2,6,1] => [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
{{1,3,6},{2,4},{5}}
=> [3,4,6,2,5,1] => [5,6,3,4,2,1] => ([(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
{{1,3},{2,5,6},{4}}
=> [3,5,1,4,6,2] => [6,5,3,1,4,2] => ([(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)
=> 6
{{1,3},{2,6},{4},{5}}
=> [3,6,1,4,5,2] => [5,6,3,1,4,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 6
{{1,4},{2,3,5,6}}
=> [4,3,5,1,6,2] => [6,5,4,3,1,2] => ([(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
{{1,4},{2,3,6},{5}}
=> [4,3,6,1,5,2] => [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
{{1,5,6},{2,3,4}}
=> [5,3,4,2,6,1] => [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
{{1,6},{2,3,4},{5}}
=> [6,3,4,2,5,1] => [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
{{1,5,6},{2,3},{4}}
=> [5,3,2,4,6,1] => [6,3,5,2,4,1] => ([(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)
=> 6
{{1,6},{2,3},{4},{5}}
=> [6,3,2,4,5,1] => [5,3,6,2,4,1] => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
{{1,4},{2,5,6},{3}}
=> [4,5,3,1,6,2] => [6,3,5,4,1,2] => ([(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
{{1,4},{2},{3,5,6}}
=> [4,2,5,1,6,3] => [6,5,4,2,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
{{1,4},{2,6},{3},{5}}
=> [4,6,3,1,5,2] => [5,3,6,4,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 6
{{1,4},{2},{3,6},{5}}
=> [4,2,6,1,5,3] => [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
{{1,5,6},{2,4},{3}}
=> [5,4,3,2,6,1] => [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
{{1,5,6},{2},{3,4}}
=> [5,2,4,3,6,1] => [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
{{1,6},{2},{3,4},{5}}
=> [6,2,4,3,5,1] => [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
{{1,5,6},{2},{3},{4}}
=> [5,2,3,4,6,1] => [6,5,2,3,4,1] => ([(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
{{1,5},{2},{3,6},{4}}
=> [5,2,6,4,1,3] => [4,6,2,5,1,3] => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
{{1,6},{2},{3},{4},{5}}
=> [6,2,3,4,5,1] => [5,6,2,3,4,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 6
Description
The pebbling number of a connected graph.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!