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Your data matches 6 different statistics following compositions of up to 3 maps.
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Matching statistic: St001060
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001060: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001060: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,1] => [3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[1,1,1,1] => [4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[2,1,1] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 2
[1,1,1,1,1] => [5] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,1,1,2] => [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[1,2,1,1] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[1,2,2] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 2
[2,1,1,1] => [1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[3,1,1] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 2
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,1,2] => [4,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,1,1,3] => [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[1,1,2,1,1] => [2,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,1,2,2] => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[1,2,1,1,1] => [1,1,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,2,2,1] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2
[1,3,1,1] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[2,1,1,1,1] => [1,4] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[2,1,1,2] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2
[2,2,1,1] => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[2,2,2] => [3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[3,1,1,1] => [1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[4,1,1] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 2
[1,1,1,1,1,2] => [5,1] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,1,1,1,3] => [4,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,1,1,2,1,1] => [3,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,2,2] => [3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,1,1,4] => [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[1,1,2,1,1,1] => [2,1,3] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,2,2,1] => [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,1,3,1,1] => [2,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,2,1,1,2] => [1,1,2,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> 3
[1,2,2,1,1] => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,2,2,2] => [1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[1,3,1,1,1] => [1,1,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,3,3] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 2
[1,4,1,1] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[2,1,1,1,1,1] => [1,5] => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[2,1,1,1,2] => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[2,1,1,3] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2
[2,1,2,1,1] => [1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 4
[2,1,2,2] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[2,2,1,1,1] => [2,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[2,2,2,1] => [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[2,3,1,1] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[3,1,1,1,1] => [1,4] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[3,1,1,2] => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> 2
[3,2,1,1] => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[3,2,2] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 2
[4,1,1,1] => [1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
Description
The distinguishing index of a graph.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
Matching statistic: St001232
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 100%
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 100%
Values
[1,1,1] => [3] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? = 3
[1,1,1,1] => [4] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? = 3
[2,1,1] => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
[1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 3
[1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> ? = 3
[1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[1,2,2] => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
[2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> ? = 2
[3,1,1] => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 2
[1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? = 3
[1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> ? = 3
[1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ? = 2
[1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2
[1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> ? = 2
[1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> ? = 2
[2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2
[2,2,2] => [3] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? = 3
[3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> ? = 2
[4,1,1] => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
[1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 3
[1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? = 3
[1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0]
=> ? = 2
[1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? = 2
[1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> ? = 3
[1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> ? = 2
[1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? = 2
[1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ? = 2
[1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3
[1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ? = 2
[1,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> ? = 2
[1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> ? = 2
[1,3,3] => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
[1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 2
[2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ? = 2
[2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 4
[2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ? = 2
[2,2,2,1] => [3,1] => [1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> ? = 3
[2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> ? = 2
[3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[3,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[3,2,2] => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
[4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> ? = 2
[5,1,1] => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
[1,1,1,1,1,3] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 3
[1,1,1,1,2,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 2
[1,1,1,1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? = 3
[1,1,1,2,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0]
=> ? = 2
[1,1,1,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0]
=> ? = 2
[1,1,1,5] => [3,1] => [1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> ? = 3
[1,1,2,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2
[1,1,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> ? = 2
[1,1,2,2,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ? = 2
[1,1,3,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> ? = 2
[1,1,3,3] => [2,2] => [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2
[1,1,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ? = 2
[1,2,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> ? = 2
[1,2,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3
[1,2,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 5
[1,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 4
[1,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> ? = 2
[1,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ? = 2
[1,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[1,2,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 4
[1,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3
[1,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 4
[1,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[1,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[1,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> ? = 2
[1,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[2,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> ? = 2
[2,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ? = 2
[2,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[2,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3
[2,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 4
[2,3,3] => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
[2,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[3,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[3,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 4
[3,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[3,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[4,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[4,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[4,2,2] => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
[6,1,1] => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
[1,2,1,1,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3
[1,2,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 4
[1,2,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 5
[1,2,2,4] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[1,2,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[1,2,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 4
[1,3,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3
[1,3,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 5
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001207
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 50%
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 50%
Values
[1,1,1] => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 3
[1,1,1,1] => [4] => [1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => ? = 3
[2,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => ? = 3
[1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3
[1,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 2
[3,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 2
[1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => ? = 3
[1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => ? = 2
[1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 2
[1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> [4,1,2,5,6,3] => ? = 2
[1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 2
[1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3
[2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 2
[2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 2
[2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 2
[2,2,2] => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 3
[3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 2
[4,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,3,4,5,7,1,6] => ? = 3
[1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => ? = 3
[1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
=> [2,3,6,1,4,7,5] => ? = 2
[1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> [2,3,5,1,6,4] => ? = 2
[1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
=> [2,5,1,3,6,7,4] => ? = 2
[1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [2,4,1,6,3,5] => ? = 2
[1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => ? = 2
[1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
=> [4,1,2,6,3,5] => ? = 3
[1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> [3,1,5,2,6,4] => ? = 2
[1,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 2
[1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> [4,1,2,5,6,3] => ? = 2
[1,3,3] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3
[2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,1,4,5,6,7,2] => ? = 2
[2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> [3,1,4,6,2,5] => ? = 2
[2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 2
[2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> [5,1,2,3,6,4] => ? = 4
[2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3
[2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> [2,4,1,5,6,3] => ? = 2
[2,2,2,1] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3
[3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 2
[3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 2
[3,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3
[3,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 2
[5,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,1,1,1,1,3] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,3,4,5,7,1,6] => ? = 3
[1,1,1,1,2,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]
=> [2,3,4,6,1,7,5] => ? = 2
[1,1,1,1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => ? = 3
[1,1,1,2,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [2,3,5,1,7,4,6] => ? = 2
[1,1,1,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
=> [2,3,6,1,4,7,5] => ? = 2
[1,1,1,5] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,1,2,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> [2,5,1,3,7,4,6] => ? = 2
[1,1,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [2,4,1,6,3,7,5] => ? = 2
[2,3,3] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[4,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[6,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,4,4] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[3,3,3] => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 3
[5,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[7,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[2,4,4] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[4,3,3] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[6,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[8,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[2,5,5] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[4,4,4] => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 3
[3,4,4] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[6,3,3] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,5,5] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
Matching statistic: St001582
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 50%
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 50%
Values
[1,1,1] => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 3
[1,1,1,1] => [4] => [1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => ? = 3
[2,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => ? = 3
[1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3
[1,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 2
[3,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 2
[1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => ? = 3
[1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => ? = 2
[1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 2
[1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> [4,1,2,5,6,3] => ? = 2
[1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 2
[1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3
[2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 2
[2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 2
[2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 2
[2,2,2] => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 3
[3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 2
[4,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,3,4,5,7,1,6] => ? = 3
[1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => ? = 3
[1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
=> [2,3,6,1,4,7,5] => ? = 2
[1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> [2,3,5,1,6,4] => ? = 2
[1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
=> [2,5,1,3,6,7,4] => ? = 2
[1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [2,4,1,6,3,5] => ? = 2
[1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => ? = 2
[1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
=> [4,1,2,6,3,5] => ? = 3
[1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> [3,1,5,2,6,4] => ? = 2
[1,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 2
[1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> [4,1,2,5,6,3] => ? = 2
[1,3,3] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3
[2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,1,4,5,6,7,2] => ? = 2
[2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> [3,1,4,6,2,5] => ? = 2
[2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 2
[2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> [5,1,2,3,6,4] => ? = 4
[2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3
[2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> [2,4,1,5,6,3] => ? = 2
[2,2,2,1] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3
[3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 2
[3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 2
[3,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3
[3,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 2
[5,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,1,1,1,1,3] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,3,4,5,7,1,6] => ? = 3
[1,1,1,1,2,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]
=> [2,3,4,6,1,7,5] => ? = 2
[1,1,1,1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => ? = 3
[1,1,1,2,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [2,3,5,1,7,4,6] => ? = 2
[1,1,1,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
=> [2,3,6,1,4,7,5] => ? = 2
[1,1,1,5] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,1,2,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> [2,5,1,3,7,4,6] => ? = 2
[1,1,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [2,4,1,6,3,7,5] => ? = 2
[2,3,3] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[4,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[6,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,4,4] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[3,3,3] => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 3
[5,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[7,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[2,4,4] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[4,3,3] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[6,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[8,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[2,5,5] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[4,4,4] => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 3
[3,4,4] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[6,3,3] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,5,5] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 2
Description
The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order.
Matching statistic: St001171
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001171: Permutations ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 50%
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001171: Permutations ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 50%
Values
[1,1,1] => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 6 = 3 + 3
[1,1,1,1] => [4] => [1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => ? = 3 + 3
[2,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => ? = 3 + 3
[1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3 + 3
[1,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 2 + 3
[3,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 2 + 3
[1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => ? = 3 + 3
[1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => ? = 2 + 3
[1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 2 + 3
[1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> [4,1,2,5,6,3] => ? = 2 + 3
[1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 2 + 3
[1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3 + 3
[2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 2 + 3
[2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 2 + 3
[2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 2 + 3
[2,2,2] => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 6 = 3 + 3
[3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 2 + 3
[4,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,3,4,5,7,1,6] => ? = 3 + 3
[1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => ? = 3 + 3
[1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
=> [2,3,6,1,4,7,5] => ? = 2 + 3
[1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> [2,3,5,1,6,4] => ? = 2 + 3
[1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
=> [2,5,1,3,6,7,4] => ? = 2 + 3
[1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [2,4,1,6,3,5] => ? = 2 + 3
[1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => ? = 2 + 3
[1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
=> [4,1,2,6,3,5] => ? = 3 + 3
[1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> [3,1,5,2,6,4] => ? = 2 + 3
[1,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 2 + 3
[1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> [4,1,2,5,6,3] => ? = 2 + 3
[1,3,3] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3 + 3
[2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,1,4,5,6,7,2] => ? = 2 + 3
[2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> [3,1,4,6,2,5] => ? = 2 + 3
[2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 2 + 3
[2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> [5,1,2,3,6,4] => ? = 4 + 3
[2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3 + 3
[2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> [2,4,1,5,6,3] => ? = 2 + 3
[2,2,2,1] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3 + 3
[3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 2 + 3
[3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 2 + 3
[3,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 3 + 3
[3,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 2 + 3
[5,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[1,1,1,1,1,3] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,3,4,5,7,1,6] => ? = 3 + 3
[1,1,1,1,2,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]
=> [2,3,4,6,1,7,5] => ? = 2 + 3
[1,1,1,1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => ? = 3 + 3
[1,1,1,2,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [2,3,5,1,7,4,6] => ? = 2 + 3
[1,1,1,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
=> [2,3,6,1,4,7,5] => ? = 2 + 3
[1,1,1,5] => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[1,1,2,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> [2,5,1,3,7,4,6] => ? = 2 + 3
[1,1,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [2,4,1,6,3,7,5] => ? = 2 + 3
[2,3,3] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[4,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[6,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[1,4,4] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[3,3,3] => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 6 = 3 + 3
[5,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[7,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[2,4,4] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[4,3,3] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[6,2,2] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[8,1,1] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[2,5,5] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[4,4,4] => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 6 = 3 + 3
[3,4,4] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[6,3,3] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[1,5,5] => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
Description
The vector space dimension of $Ext_A^1(I_o,A)$ when $I_o$ is the tilting module corresponding to the permutation $o$ in the Auslander algebra $A$ of $K[x]/(x^n)$.
Matching statistic: St001645
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00173: Integer compositions —rotate front to back⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 25%
Mp00173: Integer compositions —rotate front to back⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 25%
Values
[1,1,1] => [3] => [3] => ([],3)
=> ? = 3 + 2
[1,1,1,1] => [4] => [4] => ([],4)
=> ? = 3 + 2
[2,1,1] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[1,1,1,1,1] => [5] => [5] => ([],5)
=> ? = 3 + 2
[1,1,1,2] => [3,1] => [1,3] => ([(2,3)],4)
=> ? = 3 + 2
[1,2,1,1] => [1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 3 + 2
[1,2,2] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[2,1,1,1] => [1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 2 + 2
[3,1,1] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[1,1,1,1,1,1] => [6] => [6] => ([],6)
=> ? = 2 + 2
[1,1,1,1,2] => [4,1] => [1,4] => ([(3,4)],5)
=> ? = 3 + 2
[1,1,1,3] => [3,1] => [1,3] => ([(2,3)],4)
=> ? = 3 + 2
[1,1,2,1,1] => [2,1,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 2
[1,1,2,2] => [2,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 + 2
[1,2,1,1,1] => [1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 2
[1,2,2,1] => [1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 2 + 2
[1,3,1,1] => [1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 3 + 2
[2,1,1,1,1] => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 2 + 2
[2,1,1,2] => [1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 2 + 2
[2,2,1,1] => [2,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 + 2
[2,2,2] => [3] => [3] => ([],3)
=> ? = 3 + 2
[3,1,1,1] => [1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 2 + 2
[4,1,1] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[1,1,1,1,1,2] => [5,1] => [1,5] => ([(4,5)],6)
=> ? = 3 + 2
[1,1,1,1,3] => [4,1] => [1,4] => ([(3,4)],5)
=> ? = 3 + 2
[1,1,1,2,1,1] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,2,2] => [3,2] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 2 + 2
[1,1,1,4] => [3,1] => [1,3] => ([(2,3)],4)
=> ? = 3 + 2
[1,1,2,1,1,1] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,2,2,1] => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 2
[1,1,3,1,1] => [2,1,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 2
[1,2,1,1,2] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 2
[1,2,2,1,1] => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 2
[1,2,2,2] => [1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 2 + 2
[1,3,1,1,1] => [1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 2
[1,3,3] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[1,4,1,1] => [1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 3 + 2
[2,1,1,1,1,1] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
[2,1,1,1,2] => [1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 2
[2,1,1,3] => [1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 2 + 2
[2,1,2,1,1] => [1,1,1,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 2
[2,1,2,2] => [1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 3 + 2
[2,2,1,1,1] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 2
[2,2,2,1] => [3,1] => [1,3] => ([(2,3)],4)
=> ? = 3 + 2
[2,3,1,1] => [1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 3 + 2
[3,1,1,1,1] => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 2 + 2
[3,1,1,2] => [1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 2 + 2
[3,2,1,1] => [1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 3 + 2
[3,2,2] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[4,1,1,1] => [1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 2 + 2
[5,1,1] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[1,1,1,1,1,3] => [5,1] => [1,5] => ([(4,5)],6)
=> ? = 3 + 2
[1,1,1,1,2,2] => [4,2] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,1,4] => [4,1] => [1,4] => ([(3,4)],5)
=> ? = 3 + 2
[1,1,1,2,2,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,3,1,1] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,5] => [3,1] => [1,3] => ([(2,3)],4)
=> ? = 3 + 2
[2,3,3] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[4,2,2] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[6,1,1] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[1,4,4] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[5,2,2] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[7,1,1] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[2,4,4] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[4,3,3] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[6,2,2] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[8,1,1] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[2,5,5] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[3,4,4] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[6,3,3] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
[1,5,5] => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4 = 2 + 2
Description
The pebbling number of a connected graph.
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