Processing math: 0%

Your data matches 6 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001060
Mp00253: Decorated permutations permutationPermutations
Mp00090: Permutations cycle-as-one-line notationPermutations
Mp00160: Permutations graph of inversionsGraphs
St001060: Graphs ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
[3,1,4,2] => [3,1,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> 2
[3,+,4,1] => [3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> 2
[3,-,4,1] => [3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> 2
[4,1,2,3] => [4,1,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[4,1,+,2] => [4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 2
[4,1,-,2] => [4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 2
[4,+,1,3] => [4,2,1,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[4,-,1,3] => [4,2,1,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[4,+,+,1] => [4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 2
[4,-,+,1] => [4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 2
[4,+,-,1] => [4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 2
[4,-,-,1] => [4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 2
[4,3,1,2] => [4,3,1,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 2
[4,3,2,1] => [4,3,2,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 2
[3,1,4,5,2] => [3,1,4,5,2] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> 3
[3,1,5,2,4] => [3,1,5,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[3,1,5,+,2] => [3,1,5,4,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> 2
[3,1,5,-,2] => [3,1,5,4,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> 2
[3,+,4,5,1] => [3,2,4,5,1] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> 3
[3,-,4,5,1] => [3,2,4,5,1] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> 3
[3,+,5,1,4] => [3,2,5,1,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[3,-,5,1,4] => [3,2,5,1,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[3,+,5,+,1] => [3,2,5,4,1] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> 2
[3,-,5,+,1] => [3,2,5,4,1] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> 2
[3,+,5,-,1] => [3,2,5,4,1] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> 2
[3,-,5,-,1] => [3,2,5,4,1] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> 2
[3,4,5,1,2] => [3,4,5,1,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> 2
[3,4,5,2,1] => [3,4,5,2,1] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> 2
[4,1,2,5,3] => [4,1,2,5,3] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[4,1,+,5,2] => [4,1,3,5,2] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 3
[4,1,-,5,2] => [4,1,3,5,2] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 3
[4,1,5,3,2] => [4,1,5,3,2] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[4,+,1,5,3] => [4,2,1,5,3] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[4,-,1,5,3] => [4,2,1,5,3] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[4,+,+,5,1] => [4,2,3,5,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 3
[4,-,+,5,1] => [4,2,3,5,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 3
[4,+,-,5,1] => [4,2,3,5,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 3
[4,-,-,5,1] => [4,2,3,5,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 3
[4,+,5,3,1] => [4,2,5,3,1] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[4,-,5,3,1] => [4,2,5,3,1] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[4,3,1,5,2] => [4,3,1,5,2] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 3
[4,3,2,5,1] => [4,3,2,5,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 3
[4,5,1,2,3] => [4,5,1,2,3] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> 2
[4,5,2,1,3] => [4,5,2,1,3] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> 2
[4,5,+,1,2] => [4,5,3,1,2] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> 2
[4,5,-,1,2] => [4,5,3,1,2] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> 2
[4,5,+,2,1] => [4,5,3,2,1] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> 2
[4,5,-,2,1] => [4,5,3,2,1] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> 2
[5,1,2,3,4] => [5,1,2,3,4] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[5,1,2,+,3] => [5,1,2,4,3] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 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: St001820
Mp00253: Decorated permutations permutationPermutations
Mp00090: Permutations cycle-as-one-line notationPermutations
Mp00208: Permutations lattice of intervalsLattices
St001820: Lattices ⟶ ℤResult quality: 11% values known / values provided: 11%distinct values known / distinct values provided: 67%
Values
[3,1,4,2] => [3,1,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 1 = 2 - 1
[3,+,4,1] => [3,2,4,1] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 1 = 2 - 1
[3,-,4,1] => [3,2,4,1] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 1 = 2 - 1
[4,1,2,3] => [4,1,2,3] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> 2 = 3 - 1
[4,1,+,2] => [4,1,3,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 1 = 2 - 1
[4,1,-,2] => [4,1,3,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 1 = 2 - 1
[4,+,1,3] => [4,2,1,3] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> 2 = 3 - 1
[4,-,1,3] => [4,2,1,3] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> 2 = 3 - 1
[4,+,+,1] => [4,2,3,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 1 = 2 - 1
[4,-,+,1] => [4,2,3,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 1 = 2 - 1
[4,+,-,1] => [4,2,3,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 1 = 2 - 1
[4,-,-,1] => [4,2,3,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 1 = 2 - 1
[4,3,1,2] => [4,3,1,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 1 = 2 - 1
[4,3,2,1] => [4,3,2,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 1 = 2 - 1
[3,1,4,5,2] => [3,1,4,5,2] => [1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[3,1,5,2,4] => [3,1,5,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? = 2 - 1
[3,1,5,+,2] => [3,1,5,4,2] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1 = 2 - 1
[3,1,5,-,2] => [3,1,5,4,2] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1 = 2 - 1
[3,+,4,5,1] => [3,2,4,5,1] => [1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[3,-,4,5,1] => [3,2,4,5,1] => [1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[3,+,5,1,4] => [3,2,5,1,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? = 2 - 1
[3,-,5,1,4] => [3,2,5,1,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? = 2 - 1
[3,+,5,+,1] => [3,2,5,4,1] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1 = 2 - 1
[3,-,5,+,1] => [3,2,5,4,1] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1 = 2 - 1
[3,+,5,-,1] => [3,2,5,4,1] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1 = 2 - 1
[3,-,5,-,1] => [3,2,5,4,1] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1 = 2 - 1
[3,4,5,1,2] => [3,4,5,1,2] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1 = 2 - 1
[3,4,5,2,1] => [3,4,5,2,1] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1 = 2 - 1
[4,1,2,5,3] => [4,1,2,5,3] => [1,4,5,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ? = 2 - 1
[4,1,+,5,2] => [4,1,3,5,2] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ? = 3 - 1
[4,1,-,5,2] => [4,1,3,5,2] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ? = 3 - 1
[4,1,5,3,2] => [4,1,5,3,2] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? = 2 - 1
[4,+,1,5,3] => [4,2,1,5,3] => [1,4,5,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ? = 2 - 1
[4,-,1,5,3] => [4,2,1,5,3] => [1,4,5,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ? = 2 - 1
[4,+,+,5,1] => [4,2,3,5,1] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ? = 3 - 1
[4,-,+,5,1] => [4,2,3,5,1] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ? = 3 - 1
[4,+,-,5,1] => [4,2,3,5,1] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ? = 3 - 1
[4,-,-,5,1] => [4,2,3,5,1] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ? = 3 - 1
[4,+,5,3,1] => [4,2,5,3,1] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? = 2 - 1
[4,-,5,3,1] => [4,2,5,3,1] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? = 2 - 1
[4,3,1,5,2] => [4,3,1,5,2] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ? = 3 - 1
[4,3,2,5,1] => [4,3,2,5,1] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ? = 3 - 1
[4,5,1,2,3] => [4,5,1,2,3] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1 = 2 - 1
[4,5,2,1,3] => [4,5,2,1,3] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1 = 2 - 1
[4,5,+,1,2] => [4,5,3,1,2] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1 = 2 - 1
[4,5,-,1,2] => [4,5,3,1,2] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1 = 2 - 1
[4,5,+,2,1] => [4,5,3,2,1] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1 = 2 - 1
[4,5,-,2,1] => [4,5,3,2,1] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1 = 2 - 1
[5,1,2,3,4] => [5,1,2,3,4] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ? = 3 - 1
[5,1,2,+,3] => [5,1,2,4,3] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? = 2 - 1
[5,1,2,-,3] => [5,1,2,4,3] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? = 2 - 1
[5,1,+,2,4] => [5,1,3,2,4] => [1,5,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ? = 2 - 1
[5,1,-,2,4] => [5,1,3,2,4] => [1,5,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ? = 2 - 1
[5,1,+,+,2] => [5,1,3,4,2] => [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[5,1,-,+,2] => [5,1,3,4,2] => [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[5,1,+,-,2] => [5,1,3,4,2] => [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[5,1,-,-,2] => [5,1,3,4,2] => [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[5,1,4,2,3] => [5,1,4,2,3] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ? = 2 - 1
[5,1,4,3,2] => [5,1,4,3,2] => [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[5,+,1,3,4] => [5,2,1,3,4] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ? = 3 - 1
[5,-,1,3,4] => [5,2,1,3,4] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ? = 3 - 1
[5,+,1,+,3] => [5,2,1,4,3] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? = 2 - 1
[5,-,1,+,3] => [5,2,1,4,3] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? = 2 - 1
[5,+,1,-,3] => [5,2,1,4,3] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? = 2 - 1
[5,-,1,-,3] => [5,2,1,4,3] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? = 2 - 1
[5,+,+,1,4] => [5,2,3,1,4] => [1,5,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ? = 2 - 1
[5,-,+,1,4] => [5,2,3,1,4] => [1,5,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ? = 2 - 1
[5,+,-,1,4] => [5,2,3,1,4] => [1,5,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ? = 2 - 1
[5,-,-,1,4] => [5,2,3,1,4] => [1,5,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ? = 2 - 1
[5,+,+,+,1] => [5,2,3,4,1] => [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[5,-,+,+,1] => [5,2,3,4,1] => [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[5,+,-,+,1] => [5,2,3,4,1] => [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[5,+,+,-,1] => [5,2,3,4,1] => [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[5,-,-,+,1] => [5,2,3,4,1] => [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[5,-,+,-,1] => [5,2,3,4,1] => [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[5,+,-,-,1] => [5,2,3,4,1] => [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[5,-,-,-,1] => [5,2,3,4,1] => [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? = 3 - 1
[5,+,4,1,3] => [5,2,4,1,3] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ? = 2 - 1
[3,1,6,2,+,4] => [3,1,6,2,5,4] => [1,3,6,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[3,1,6,2,-,4] => [3,1,6,2,5,4] => [1,3,6,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[3,+,6,1,+,4] => [3,2,6,1,5,4] => [1,3,6,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[3,-,6,1,+,4] => [3,2,6,1,5,4] => [1,3,6,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[3,+,6,1,-,4] => [3,2,6,1,5,4] => [1,3,6,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[3,-,6,1,-,4] => [3,2,6,1,5,4] => [1,3,6,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[3,5,6,1,2,4] => [3,5,6,1,2,4] => [1,3,6,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[3,5,6,2,1,4] => [3,5,6,2,1,4] => [1,3,6,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[3,6,5,1,2,4] => [3,6,5,1,2,4] => [1,3,5,2,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[3,6,5,2,1,4] => [3,6,5,2,1,4] => [1,3,5,2,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[3,6,5,+,1,2] => [3,6,5,4,1,2] => [1,3,5,2,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[3,6,5,-,1,2] => [3,6,5,4,1,2] => [1,3,5,2,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[3,6,5,+,2,1] => [3,6,5,4,2,1] => [1,3,5,2,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[3,6,5,-,2,1] => [3,6,5,4,2,1] => [1,3,5,2,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[4,5,1,6,3,2] => [4,5,1,6,3,2] => [1,4,6,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[4,5,2,6,3,1] => [4,5,2,6,3,1] => [1,4,6,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[4,5,+,6,1,2] => [4,5,3,6,1,2] => [1,4,6,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[4,5,-,6,1,2] => [4,5,3,6,1,2] => [1,4,6,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[4,5,+,6,2,1] => [4,5,3,6,2,1] => [1,4,6,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[4,5,-,6,2,1] => [4,5,3,6,2,1] => [1,4,6,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[4,6,1,2,+,3] => [4,6,1,2,5,3] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
[4,6,1,2,-,3] => [4,6,1,2,5,3] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 1 = 2 - 1
Description
The size of the image of the pop stack sorting operator. The pop stack sorting operator is defined by PopL(x)=x{yLy. This statistic returns the size of Pop_L^\downarrow(L)\}.
Matching statistic: St001198
Mp00253: Decorated permutations permutationPermutations
Mp00159: Permutations Demazure product with inversePermutations
Mp00127: Permutations left-to-right-maxima to Dyck pathDyck paths
St001198: Dyck paths ⟶ ℤResult quality: 8% values known / values provided: 8%distinct values known / distinct values provided: 33%
Values
[3,1,4,2] => [3,1,4,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[3,+,4,1] => [3,2,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[3,-,4,1] => [3,2,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,1,2,3] => [4,1,2,3] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 3
[4,1,+,2] => [4,1,3,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,1,-,2] => [4,1,3,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,+,1,3] => [4,2,1,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 3
[4,-,1,3] => [4,2,1,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 3
[4,+,+,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,-,+,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,+,-,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,-,-,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,3,1,2] => [4,3,1,2] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[3,1,4,5,2] => [3,1,4,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[3,1,5,2,4] => [3,1,5,2,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 2
[3,1,5,+,2] => [3,1,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,1,5,-,2] => [3,1,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,+,4,5,1] => [3,2,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[3,-,4,5,1] => [3,2,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[3,+,5,1,4] => [3,2,5,1,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 2
[3,-,5,1,4] => [3,2,5,1,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 2
[3,+,5,+,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,-,5,+,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,+,5,-,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,-,5,-,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,4,5,1,2] => [3,4,5,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,4,5,2,1] => [3,4,5,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,1,2,5,3] => [4,1,2,5,3] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,1,+,5,2] => [4,1,3,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,1,-,5,2] => [4,1,3,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,1,5,3,2] => [4,1,5,3,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,+,1,5,3] => [4,2,1,5,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,-,1,5,3] => [4,2,1,5,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,+,+,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,-,+,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,+,-,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,-,-,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,+,5,3,1] => [4,2,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,-,5,3,1] => [4,2,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,3,1,5,2] => [4,3,1,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,3,2,5,1] => [4,3,2,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,5,1,2,3] => [4,5,1,2,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,5,2,1,3] => [4,5,2,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,5,+,1,2] => [4,5,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,5,-,1,2] => [4,5,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,5,+,2,1] => [4,5,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,5,-,2,1] => [4,5,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[5,1,2,3,4] => [5,1,2,3,4] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[5,1,2,+,3] => [5,1,2,4,3] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[5,1,2,-,3] => [5,1,2,4,3] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[5,1,+,2,4] => [5,1,3,2,4] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[5,1,-,2,4] => [5,1,3,2,4] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,1,4,6,2,5] => [3,1,4,6,2,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[3,1,5,2,6,4] => [3,1,5,2,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,1,6,2,4,5] => [3,1,6,2,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,1,6,2,+,4] => [3,1,6,2,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,1,6,2,-,4] => [3,1,6,2,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,1,6,+,2,5] => [3,1,6,4,2,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,1,6,-,2,5] => [3,1,6,4,2,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,1,6,5,2,4] => [3,1,6,5,2,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,+,4,6,1,5] => [3,2,4,6,1,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[3,-,4,6,1,5] => [3,2,4,6,1,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[3,+,5,1,6,4] => [3,2,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,-,5,1,6,4] => [3,2,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,+,6,1,4,5] => [3,2,6,1,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,-,6,1,4,5] => [3,2,6,1,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,+,6,1,+,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,-,6,1,+,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,+,6,1,-,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,-,6,1,-,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,+,6,+,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,-,6,+,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,+,6,-,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,-,6,-,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,+,6,5,1,4] => [3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,-,6,5,1,4] => [3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,4,6,1,2,5] => [3,4,6,1,2,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,4,6,2,1,5] => [3,4,6,2,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,5,6,1,2,4] => [3,5,6,1,2,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
[3,5,6,2,1,4] => [3,5,6,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
[3,6,5,1,2,4] => [3,6,5,1,2,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
[3,6,5,2,1,4] => [3,6,5,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
[4,1,2,6,3,5] => [4,1,2,6,3,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,1,+,6,2,5] => [4,1,3,6,2,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,1,-,6,2,5] => [4,1,3,6,2,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,1,6,3,2,5] => [4,1,6,3,2,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[4,+,1,6,3,5] => [4,2,1,6,3,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,-,1,6,3,5] => [4,2,1,6,3,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,+,+,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,-,+,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,+,-,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,-,-,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,+,6,3,1,5] => [4,2,6,3,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[4,-,6,3,1,5] => [4,2,6,3,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[4,3,1,6,2,5] => [4,3,1,6,2,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,3,2,6,1,5] => [4,3,2,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,6,1,2,3,5] => [4,6,1,2,3,5] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
[4,6,2,1,3,5] => [4,6,2,1,3,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
[4,6,+,1,2,5] => [4,6,3,1,2,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
Description
The number of simple modules in the algebra eAe with projective dimension at most 1 in the corresponding Nakayama algebra A with minimal faithful projective-injective module eA.
Matching statistic: St001206
Mp00253: Decorated permutations permutationPermutations
Mp00159: Permutations Demazure product with inversePermutations
Mp00127: Permutations left-to-right-maxima to Dyck pathDyck paths
St001206: Dyck paths ⟶ ℤResult quality: 8% values known / values provided: 8%distinct values known / distinct values provided: 33%
Values
[3,1,4,2] => [3,1,4,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[3,+,4,1] => [3,2,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[3,-,4,1] => [3,2,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,1,2,3] => [4,1,2,3] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 3
[4,1,+,2] => [4,1,3,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,1,-,2] => [4,1,3,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,+,1,3] => [4,2,1,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 3
[4,-,1,3] => [4,2,1,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 3
[4,+,+,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,-,+,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,+,-,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,-,-,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,3,1,2] => [4,3,1,2] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2
[3,1,4,5,2] => [3,1,4,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[3,1,5,2,4] => [3,1,5,2,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 2
[3,1,5,+,2] => [3,1,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,1,5,-,2] => [3,1,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,+,4,5,1] => [3,2,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[3,-,4,5,1] => [3,2,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[3,+,5,1,4] => [3,2,5,1,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 2
[3,-,5,1,4] => [3,2,5,1,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 2
[3,+,5,+,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,-,5,+,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,+,5,-,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,-,5,-,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,4,5,1,2] => [3,4,5,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,4,5,2,1] => [3,4,5,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,1,2,5,3] => [4,1,2,5,3] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,1,+,5,2] => [4,1,3,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,1,-,5,2] => [4,1,3,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,1,5,3,2] => [4,1,5,3,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,+,1,5,3] => [4,2,1,5,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,-,1,5,3] => [4,2,1,5,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,+,+,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,-,+,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,+,-,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,-,-,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,+,5,3,1] => [4,2,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,-,5,3,1] => [4,2,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,3,1,5,2] => [4,3,1,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,3,2,5,1] => [4,3,2,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[4,5,1,2,3] => [4,5,1,2,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,5,2,1,3] => [4,5,2,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,5,+,1,2] => [4,5,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,5,-,1,2] => [4,5,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,5,+,2,1] => [4,5,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[4,5,-,2,1] => [4,5,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[5,1,2,3,4] => [5,1,2,3,4] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3
[5,1,2,+,3] => [5,1,2,4,3] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[5,1,2,-,3] => [5,1,2,4,3] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[5,1,+,2,4] => [5,1,3,2,4] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[5,1,-,2,4] => [5,1,3,2,4] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2
[3,1,4,6,2,5] => [3,1,4,6,2,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[3,1,5,2,6,4] => [3,1,5,2,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,1,6,2,4,5] => [3,1,6,2,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,1,6,2,+,4] => [3,1,6,2,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,1,6,2,-,4] => [3,1,6,2,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,1,6,+,2,5] => [3,1,6,4,2,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,1,6,-,2,5] => [3,1,6,4,2,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,1,6,5,2,4] => [3,1,6,5,2,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,+,4,6,1,5] => [3,2,4,6,1,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[3,-,4,6,1,5] => [3,2,4,6,1,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[3,+,5,1,6,4] => [3,2,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,-,5,1,6,4] => [3,2,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,+,6,1,4,5] => [3,2,6,1,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,-,6,1,4,5] => [3,2,6,1,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,+,6,1,+,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,-,6,1,+,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,+,6,1,-,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,-,6,1,-,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[3,+,6,+,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,-,6,+,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,+,6,-,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,-,6,-,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,+,6,5,1,4] => [3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,-,6,5,1,4] => [3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,4,6,1,2,5] => [3,4,6,1,2,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,4,6,2,1,5] => [3,4,6,2,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[3,5,6,1,2,4] => [3,5,6,1,2,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
[3,5,6,2,1,4] => [3,5,6,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
[3,6,5,1,2,4] => [3,6,5,1,2,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
[3,6,5,2,1,4] => [3,6,5,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
[4,1,2,6,3,5] => [4,1,2,6,3,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,1,+,6,2,5] => [4,1,3,6,2,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,1,-,6,2,5] => [4,1,3,6,2,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,1,6,3,2,5] => [4,1,6,3,2,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[4,+,1,6,3,5] => [4,2,1,6,3,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,-,1,6,3,5] => [4,2,1,6,3,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,+,+,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,-,+,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,+,-,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,-,-,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,+,6,3,1,5] => [4,2,6,3,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[4,-,6,3,1,5] => [4,2,6,3,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
[4,3,1,6,2,5] => [4,3,1,6,2,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,3,2,6,1,5] => [4,3,2,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
[4,6,1,2,3,5] => [4,6,1,2,3,5] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
[4,6,2,1,3,5] => [4,6,2,1,3,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
[4,6,+,1,2,5] => [4,6,3,1,2,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
Description
The maximal dimension of an indecomposable projective eAe-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module eA.
Matching statistic: St001199
Mp00253: Decorated permutations permutationPermutations
Mp00159: Permutations Demazure product with inversePermutations
Mp00127: Permutations left-to-right-maxima to Dyck pathDyck paths
St001199: Dyck paths ⟶ ℤResult quality: 8% values known / values provided: 8%distinct values known / distinct values provided: 33%
Values
[3,1,4,2] => [3,1,4,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 1
[3,+,4,1] => [3,2,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 1
[3,-,4,1] => [3,2,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 1
[4,1,2,3] => [4,1,2,3] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 3 - 1
[4,1,+,2] => [4,1,3,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 1
[4,1,-,2] => [4,1,3,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 1
[4,+,1,3] => [4,2,1,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 3 - 1
[4,-,1,3] => [4,2,1,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 3 - 1
[4,+,+,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 1
[4,-,+,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 1
[4,+,-,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 1
[4,-,-,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 1
[4,3,1,2] => [4,3,1,2] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 1
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 1
[3,1,4,5,2] => [3,1,4,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 1
[3,1,5,2,4] => [3,1,5,2,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 2 - 1
[3,1,5,+,2] => [3,1,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[3,1,5,-,2] => [3,1,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[3,+,4,5,1] => [3,2,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 1
[3,-,4,5,1] => [3,2,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 1
[3,+,5,1,4] => [3,2,5,1,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 2 - 1
[3,-,5,1,4] => [3,2,5,1,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 1 = 2 - 1
[3,+,5,+,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[3,-,5,+,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[3,+,5,-,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[3,-,5,-,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[3,4,5,1,2] => [3,4,5,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[3,4,5,2,1] => [3,4,5,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[4,1,2,5,3] => [4,1,2,5,3] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[4,1,+,5,2] => [4,1,3,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 1
[4,1,-,5,2] => [4,1,3,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 1
[4,1,5,3,2] => [4,1,5,3,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[4,+,1,5,3] => [4,2,1,5,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[4,-,1,5,3] => [4,2,1,5,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[4,+,+,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 1
[4,-,+,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 1
[4,+,-,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 1
[4,-,-,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 1
[4,+,5,3,1] => [4,2,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[4,-,5,3,1] => [4,2,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[4,3,1,5,2] => [4,3,1,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 1
[4,3,2,5,1] => [4,3,2,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 1
[4,5,1,2,3] => [4,5,1,2,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[4,5,2,1,3] => [4,5,2,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[4,5,+,1,2] => [4,5,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[4,5,-,1,2] => [4,5,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[4,5,+,2,1] => [4,5,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[4,5,-,2,1] => [4,5,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[5,1,2,3,4] => [5,1,2,3,4] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 1
[5,1,2,+,3] => [5,1,2,4,3] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[5,1,2,-,3] => [5,1,2,4,3] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[5,1,+,2,4] => [5,1,3,2,4] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[5,1,-,2,4] => [5,1,3,2,4] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[3,1,4,6,2,5] => [3,1,4,6,2,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 2 - 1
[3,1,5,2,6,4] => [3,1,5,2,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 2 - 1
[3,1,6,2,4,5] => [3,1,6,2,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 2 - 1
[3,1,6,2,+,4] => [3,1,6,2,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 2 - 1
[3,1,6,2,-,4] => [3,1,6,2,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 2 - 1
[3,1,6,+,2,5] => [3,1,6,4,2,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 2 - 1
[3,1,6,-,2,5] => [3,1,6,4,2,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 2 - 1
[3,1,6,5,2,4] => [3,1,6,5,2,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 2 - 1
[3,+,4,6,1,5] => [3,2,4,6,1,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 2 - 1
[3,-,4,6,1,5] => [3,2,4,6,1,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 2 - 1
[3,+,5,1,6,4] => [3,2,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 2 - 1
[3,-,5,1,6,4] => [3,2,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 2 - 1
[3,+,6,1,4,5] => [3,2,6,1,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 2 - 1
[3,-,6,1,4,5] => [3,2,6,1,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 2 - 1
[3,+,6,1,+,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 2 - 1
[3,-,6,1,+,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 2 - 1
[3,+,6,1,-,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 2 - 1
[3,-,6,1,-,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 2 - 1
[3,+,6,+,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 2 - 1
[3,-,6,+,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 2 - 1
[3,+,6,-,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 2 - 1
[3,-,6,-,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 2 - 1
[3,+,6,5,1,4] => [3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 2 - 1
[3,-,6,5,1,4] => [3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 2 - 1
[3,4,6,1,2,5] => [3,4,6,1,2,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 2 - 1
[3,4,6,2,1,5] => [3,4,6,2,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 2 - 1
[3,5,6,1,2,4] => [3,5,6,1,2,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 2 - 1
[3,5,6,2,1,4] => [3,5,6,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 2 - 1
[3,6,5,1,2,4] => [3,6,5,1,2,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 2 - 1
[3,6,5,2,1,4] => [3,6,5,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 2 - 1
[4,1,2,6,3,5] => [4,1,2,6,3,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 2 - 1
[4,1,+,6,2,5] => [4,1,3,6,2,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 2 - 1
[4,1,-,6,2,5] => [4,1,3,6,2,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 2 - 1
[4,1,6,3,2,5] => [4,1,6,3,2,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 2 - 1
[4,+,1,6,3,5] => [4,2,1,6,3,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 2 - 1
[4,-,1,6,3,5] => [4,2,1,6,3,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 2 - 1
[4,+,+,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 2 - 1
[4,-,+,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 2 - 1
[4,+,-,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 2 - 1
[4,-,-,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 2 - 1
[4,+,6,3,1,5] => [4,2,6,3,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 2 - 1
[4,-,6,3,1,5] => [4,2,6,3,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 2 - 1
[4,3,1,6,2,5] => [4,3,1,6,2,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 2 - 1
[4,3,2,6,1,5] => [4,3,2,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 2 - 1
[4,6,1,2,3,5] => [4,6,1,2,3,5] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 2 - 1
[4,6,2,1,3,5] => [4,6,2,1,3,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 2 - 1
[4,6,+,1,2,5] => [4,6,3,1,2,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 2 - 1
Description
The dominant dimension of eAe for the corresponding Nakayama algebra A with minimal faithful projective-injective module eA.
Matching statistic: St001498
Mp00253: Decorated permutations permutationPermutations
Mp00159: Permutations Demazure product with inversePermutations
Mp00127: Permutations left-to-right-maxima to Dyck pathDyck paths
St001498: Dyck paths ⟶ ℤResult quality: 8% values known / values provided: 8%distinct values known / distinct values provided: 33%
Values
[3,1,4,2] => [3,1,4,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 2
[3,+,4,1] => [3,2,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 2
[3,-,4,1] => [3,2,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 2
[4,1,2,3] => [4,1,2,3] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 3 - 2
[4,1,+,2] => [4,1,3,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 2
[4,1,-,2] => [4,1,3,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 2
[4,+,1,3] => [4,2,1,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 3 - 2
[4,-,1,3] => [4,2,1,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 3 - 2
[4,+,+,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 2
[4,-,+,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 2
[4,+,-,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 2
[4,-,-,1] => [4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 2
[4,3,1,2] => [4,3,1,2] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 2
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? = 2 - 2
[3,1,4,5,2] => [3,1,4,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 2
[3,1,5,2,4] => [3,1,5,2,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 0 = 2 - 2
[3,1,5,+,2] => [3,1,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[3,1,5,-,2] => [3,1,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[3,+,4,5,1] => [3,2,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 2
[3,-,4,5,1] => [3,2,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 2
[3,+,5,1,4] => [3,2,5,1,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 0 = 2 - 2
[3,-,5,1,4] => [3,2,5,1,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 0 = 2 - 2
[3,+,5,+,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[3,-,5,+,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[3,+,5,-,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[3,-,5,-,1] => [3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[3,4,5,1,2] => [3,4,5,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[3,4,5,2,1] => [3,4,5,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[4,1,2,5,3] => [4,1,2,5,3] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[4,1,+,5,2] => [4,1,3,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 2
[4,1,-,5,2] => [4,1,3,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 2
[4,1,5,3,2] => [4,1,5,3,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[4,+,1,5,3] => [4,2,1,5,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[4,-,1,5,3] => [4,2,1,5,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[4,+,+,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 2
[4,-,+,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 2
[4,+,-,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 2
[4,-,-,5,1] => [4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 2
[4,+,5,3,1] => [4,2,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[4,-,5,3,1] => [4,2,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[4,3,1,5,2] => [4,3,1,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 2
[4,3,2,5,1] => [4,3,2,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 2
[4,5,1,2,3] => [4,5,1,2,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[4,5,2,1,3] => [4,5,2,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[4,5,+,1,2] => [4,5,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[4,5,-,1,2] => [4,5,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[4,5,+,2,1] => [4,5,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[4,5,-,2,1] => [4,5,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[5,1,2,3,4] => [5,1,2,3,4] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 2
[5,1,2,+,3] => [5,1,2,4,3] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[5,1,2,-,3] => [5,1,2,4,3] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[5,1,+,2,4] => [5,1,3,2,4] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[5,1,-,2,4] => [5,1,3,2,4] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 2
[3,1,4,6,2,5] => [3,1,4,6,2,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0 = 2 - 2
[3,1,5,2,6,4] => [3,1,5,2,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[3,1,6,2,4,5] => [3,1,6,2,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[3,1,6,2,+,4] => [3,1,6,2,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[3,1,6,2,-,4] => [3,1,6,2,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[3,1,6,+,2,5] => [3,1,6,4,2,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 2 - 2
[3,1,6,-,2,5] => [3,1,6,4,2,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 2 - 2
[3,1,6,5,2,4] => [3,1,6,5,2,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 2 - 2
[3,+,4,6,1,5] => [3,2,4,6,1,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0 = 2 - 2
[3,-,4,6,1,5] => [3,2,4,6,1,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0 = 2 - 2
[3,+,5,1,6,4] => [3,2,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[3,-,5,1,6,4] => [3,2,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[3,+,6,1,4,5] => [3,2,6,1,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[3,-,6,1,4,5] => [3,2,6,1,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[3,+,6,1,+,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[3,-,6,1,+,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[3,+,6,1,-,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[3,-,6,1,-,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[3,+,6,+,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 2 - 2
[3,-,6,+,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 2 - 2
[3,+,6,-,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 2 - 2
[3,-,6,-,1,5] => [3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 2 - 2
[3,+,6,5,1,4] => [3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 2 - 2
[3,-,6,5,1,4] => [3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 2 - 2
[3,4,6,1,2,5] => [3,4,6,1,2,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 2 - 2
[3,4,6,2,1,5] => [3,4,6,2,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 2 - 2
[3,5,6,1,2,4] => [3,5,6,1,2,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0 = 2 - 2
[3,5,6,2,1,4] => [3,5,6,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0 = 2 - 2
[3,6,5,1,2,4] => [3,6,5,1,2,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0 = 2 - 2
[3,6,5,2,1,4] => [3,6,5,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0 = 2 - 2
[4,1,2,6,3,5] => [4,1,2,6,3,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0 = 2 - 2
[4,1,+,6,2,5] => [4,1,3,6,2,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0 = 2 - 2
[4,1,-,6,2,5] => [4,1,3,6,2,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0 = 2 - 2
[4,1,6,3,2,5] => [4,1,6,3,2,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 2 - 2
[4,+,1,6,3,5] => [4,2,1,6,3,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0 = 2 - 2
[4,-,1,6,3,5] => [4,2,1,6,3,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0 = 2 - 2
[4,+,+,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0 = 2 - 2
[4,-,+,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0 = 2 - 2
[4,+,-,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0 = 2 - 2
[4,-,-,6,1,5] => [4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0 = 2 - 2
[4,+,6,3,1,5] => [4,2,6,3,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 2 - 2
[4,-,6,3,1,5] => [4,2,6,3,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 2 - 2
[4,3,1,6,2,5] => [4,3,1,6,2,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0 = 2 - 2
[4,3,2,6,1,5] => [4,3,2,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0 = 2 - 2
[4,6,1,2,3,5] => [4,6,1,2,3,5] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0 = 2 - 2
[4,6,2,1,3,5] => [4,6,2,1,3,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0 = 2 - 2
[4,6,+,1,2,5] => [4,6,3,1,2,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0 = 2 - 2
Description
The normalised height of a Nakayama algebra with magnitude 1. We use the bijection (see code) suggested by Christian Stump, to have a bijection between such Nakayama algebras with magnitude 1 and Dyck paths. The normalised height is the height of the (periodic) Dyck path given by the top of the Auslander-Reiten quiver. Thus when having a CNakayama algebra it is the Loewy length minus the number of simple modules and for the LNakayama algebras it is the usual height.