searching the database
Your data matches 145 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: St001621
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001621: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001621: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2,1],[2]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2,1],[2]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0]
=> [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0]
=> [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [[4,4,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [[4,4,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [[4,3,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [[4,3,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0]
=> [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 1
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0]
=> [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [[4,3,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [[4,4,3],[3,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [[4,4,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [[4,4,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [[4,3,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [[4,4,3],[3,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [[4,4,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [[4,4,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [[3,3,2,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [[3,3,2,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0]
=> [[4,3,2],[2]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [[4,4,2],[2]]
=> ([(0,2),(2,1)],3)
=> 1
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [[4,4,2],[2]]
=> ([(0,2),(2,1)],3)
=> 1
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [[4,3,2],[1]]
=> ([(0,2),(2,1)],3)
=> 1
Description
The number of atoms of a lattice.
An element of a lattice is an '''atom''' if it covers the least element.
Matching statistic: St001878
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2,1],[2]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2,1],[2]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0]
=> [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0]
=> [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [[4,4,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [[4,4,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [[4,3,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [[4,3,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0]
=> [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 1
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0]
=> [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [[4,3,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [[4,4,3],[3,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [[4,4,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [[4,4,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [[4,3,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [[4,4,3],[3,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [[4,4,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [[4,4,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [[3,3,2,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [[3,3,2,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0]
=> [[4,3,2],[2]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [[4,4,2],[2]]
=> ([(0,2),(2,1)],3)
=> 1
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [[4,4,2],[2]]
=> ([(0,2),(2,1)],3)
=> 1
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [[4,3,2],[1]]
=> ([(0,2),(2,1)],3)
=> 1
Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
Matching statistic: St001199
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 50% ●values known / values provided: 61%●distinct values known / distinct values provided: 50%
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 50% ●values known / values provided: 61%●distinct values known / distinct values provided: 50%
Values
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,5,2,7,3,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,2,7,3,6,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,2,7,4,3,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,2,7,4,6,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,2,7,6,3,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,2,7,6,4,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,3,7,2,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,3,7,2,6,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,3,7,4,2,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,3,7,4,6,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,3,7,6,2,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,3,7,6,4,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,4,7,2,3,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,4,7,2,6,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,4,7,3,2,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,4,7,3,6,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,4,7,6,2,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[1,5,4,7,6,3,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[2,4,1,7,3,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1
[2,4,1,7,3,6,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1
[2,4,1,7,5,3,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1
[2,4,1,7,5,6,3] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1
[2,4,1,7,6,3,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1
[2,4,1,7,6,5,3] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1
[2,4,3,7,1,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1
[2,4,3,7,1,6,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1
[2,4,3,7,5,1,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1
[2,4,3,7,5,6,1] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1
[2,4,3,7,6,1,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1
[2,4,3,7,6,5,1] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1
[2,4,6,1,3,7,5] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 1
[2,4,6,1,5,7,3] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 1
[2,4,6,1,7,3,5] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 1
[2,4,6,1,7,5,3] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 1
[2,4,6,3,1,7,5] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 1
[2,4,6,3,5,7,1] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 1
[2,4,6,3,7,1,5] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 1
[2,4,6,3,7,5,1] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 1
[2,4,6,5,1,7,3] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 1
[2,4,6,5,3,7,1] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 1
[2,4,6,5,7,1,3] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 1
[2,4,6,5,7,3,1] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 1
[2,5,1,3,7,4,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 1
[2,5,1,3,7,6,4] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 1
[2,5,1,4,7,3,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 1
[2,5,1,4,7,6,3] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 1
[2,5,1,6,3,7,4] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 1
[2,5,1,6,4,7,3] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 1
[2,5,1,7,3,4,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
[2,5,1,7,3,6,4] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 1
Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St001498
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
St001498: Dyck paths ⟶ ℤResult quality: 50% ●values known / values provided: 61%●distinct values known / distinct values provided: 50%
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
St001498: Dyck paths ⟶ ℤResult quality: 50% ●values known / values provided: 61%●distinct values known / distinct values provided: 50%
Values
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 - 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 - 1
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 1
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 1
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 1
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 1
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 1
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,5,2,7,3,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,2,7,3,6,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,2,7,4,3,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,2,7,4,6,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,2,7,6,3,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,2,7,6,4,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,3,7,2,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,3,7,2,6,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,3,7,4,2,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,3,7,4,6,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,3,7,6,2,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,3,7,6,4,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,4,7,2,3,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,4,7,2,6,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,4,7,3,2,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,4,7,3,6,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,4,7,6,2,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,5,4,7,6,3,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,1,7,3,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,1,7,3,6,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,1,7,5,3,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,1,7,5,6,3] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,1,7,6,3,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,1,7,6,5,3] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,3,7,1,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,3,7,1,6,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,3,7,5,1,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,3,7,5,6,1] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,3,7,6,1,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,3,7,6,5,1] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,6,1,3,7,5] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,6,1,5,7,3] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,6,1,7,3,5] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,6,1,7,5,3] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,6,3,1,7,5] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,6,3,5,7,1] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,6,3,7,1,5] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,6,3,7,5,1] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,6,5,1,7,3] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,6,5,3,7,1] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,6,5,7,1,3] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,4,6,5,7,3,1] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,5,1,3,7,4,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,5,1,3,7,6,4] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,5,1,4,7,3,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,5,1,4,7,6,3] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,5,1,6,3,7,4] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,5,1,6,4,7,3] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
[2,5,1,7,3,4,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
[2,5,1,7,3,6,4] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> 0 = 1 - 1
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.
Matching statistic: St001195
(load all 8 compositions to match this statistic)
(load all 8 compositions to match this statistic)
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001195: Dyck paths ⟶ ℤResult quality: 50% ●values known / values provided: 56%●distinct values known / distinct values provided: 50%
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001195: Dyck paths ⟶ ℤResult quality: 50% ●values known / values provided: 56%●distinct values known / distinct values provided: 50%
Values
[1,3,2,5,4] => [2,5,1,3,4] => [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> 1
[2,1,4,3,5] => [1,4,2,3,5] => [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> 1
[1,2,4,3,5,6] => [4,1,2,3,5,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[1,2,4,3,6,5] => [3,6,1,2,4,5] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[1,3,2,4,6,5] => [2,6,1,3,4,5] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2
[1,3,2,5,4,6] => [2,5,1,3,4,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[1,3,2,5,6,4] => [2,4,6,1,3,5] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[1,3,2,6,4,5] => [2,5,6,1,3,4] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[1,3,2,6,5,4] => [6,2,5,1,3,4] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[1,3,4,2,6,5] => [2,3,6,1,4,5] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2
[1,3,5,2,4,6] => [2,4,5,1,3,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[1,3,5,2,6,4] => [6,2,4,1,3,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[1,3,5,4,2,6] => [5,2,4,1,3,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[1,3,5,4,6,2] => [4,2,3,6,1,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[1,4,2,3,6,5] => [6,3,1,2,4,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[1,4,2,5,3,6] => [5,3,1,2,4,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[1,4,2,6,3,5] => [5,2,6,1,3,4] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[1,4,2,6,5,3] => [2,6,5,1,3,4] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[1,4,3,2,6,5] => [3,2,6,1,4,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[1,4,3,5,2,6] => [3,2,5,1,4,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[1,4,3,6,2,5] => [3,2,5,6,1,4] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[1,4,3,6,5,2] => [2,6,3,5,1,4] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[2,1,3,5,4,6] => [1,5,2,3,4,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2
[2,1,4,3,5,6] => [1,4,2,3,5,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,4,3,6,5] => [1,3,6,2,4,5] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2
[2,1,4,5,3,6] => [1,3,5,2,4,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2
[2,1,4,6,3,5] => [1,3,5,6,2,4] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,4,6,5,3] => [6,1,3,5,2,4] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[2,1,5,3,4,6] => [1,4,5,2,3,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,5,3,6,4] => [6,1,4,2,3,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[2,1,5,4,3,6] => [5,1,4,2,3,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[2,1,5,4,6,3] => [4,1,3,6,2,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[2,3,1,5,4,6] => [1,2,5,3,4,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,3,1,5,6,4] => [1,2,4,6,3,5] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,4,1,3,6,5] => [6,1,3,2,4,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[2,4,1,5,3,6] => [5,1,3,2,4,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[2,4,1,6,3,5] => [5,1,2,6,3,4] => [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1
[2,4,1,6,5,3] => [2,6,1,5,3,4] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[2,4,3,1,6,5] => [3,1,2,6,4,5] => [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1
[2,4,3,5,1,6] => [3,1,2,5,4,6] => [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1
[2,4,3,6,1,5] => [3,1,2,5,6,4] => [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1
[2,4,3,6,5,1] => [2,6,1,3,5,4] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[3,1,2,5,4,6] => [5,2,1,3,4,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[3,1,2,6,4,5] => [5,1,6,2,3,4] => [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1
[3,1,2,6,5,4] => [1,6,5,2,3,4] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[3,1,4,2,6,5] => [3,1,6,2,4,5] => [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1
[3,1,4,6,2,5] => [3,1,5,6,2,4] => [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1
[3,1,4,6,5,2] => [1,6,3,5,2,4] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[3,1,5,2,4,6] => [4,1,5,2,3,6] => [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1
[3,1,5,2,6,4] => [1,6,4,2,3,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[3,1,5,4,2,6] => [1,5,4,2,3,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[3,1,5,4,6,2] => [1,4,3,6,2,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[3,2,1,5,4,6] => [2,1,5,3,4,6] => [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1
[3,2,1,6,4,5] => [2,1,5,6,3,4] => [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1
[3,2,1,6,5,4] => [1,6,2,5,3,4] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[3,2,4,1,6,5] => [2,1,3,6,4,5] => [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1
[3,2,4,6,1,5] => [2,1,3,5,6,4] => [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1
[3,2,4,6,5,1] => [1,6,2,3,5,4] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[3,2,5,1,4,6] => [2,1,4,5,3,6] => [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1
[3,2,5,1,6,4] => [1,6,2,4,3,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[3,2,5,4,1,6] => [1,5,2,4,3,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1
[3,2,5,4,6,1] => [1,4,2,3,6,5] => [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1
[1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[1,2,3,5,4,7,6] => [4,7,1,2,3,5,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[1,2,4,3,5,7,6] => [3,7,1,2,4,5,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[1,2,4,3,6,5,7] => [3,6,1,2,4,5,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[1,2,4,3,6,7,5] => [3,5,7,1,2,4,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[1,2,4,5,3,6,7] => [3,5,1,2,4,6,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[1,2,4,5,3,7,6] => [3,4,7,1,2,5,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[1,3,2,4,5,7,6] => [2,7,1,3,4,5,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[1,3,2,4,6,5,7] => [2,6,1,3,4,5,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[1,3,2,4,6,7,5] => [2,5,7,1,3,4,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[1,3,2,5,4,6,7] => [2,5,1,3,4,6,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[1,3,2,5,4,7,6] => [2,4,7,1,3,5,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[1,3,2,5,6,4,7] => [2,4,6,1,3,5,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[1,3,2,5,6,7,4] => [2,4,5,7,1,3,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[1,3,4,2,5,7,6] => [2,3,7,1,4,5,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[1,3,4,2,6,5,7] => [2,3,6,1,4,5,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[1,3,4,2,6,7,5] => [2,3,5,7,1,4,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[1,3,4,5,2,7,6] => [2,3,4,7,1,5,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[1,5,2,7,3,4,6] => [5,6,2,7,1,3,4] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 1
[1,5,2,7,3,6,4] => [7,5,2,6,1,3,4] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1
[1,5,2,7,4,3,6] => [6,5,2,7,1,3,4] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1
[1,5,2,7,4,6,3] => [5,2,7,6,1,3,4] => [3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> 1
[1,5,2,7,6,3,4] => [6,2,7,5,1,3,4] => [3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> 1
[1,5,3,7,2,4,6] => [3,5,2,6,7,1,4] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 1
[2,1,3,4,6,5,7] => [1,6,2,3,4,5,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[2,1,3,5,4,6,7] => [1,5,2,3,4,6,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[2,1,3,5,4,7,6] => [1,4,7,2,3,5,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[2,1,3,5,6,4,7] => [1,4,6,2,3,5,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[2,1,4,3,5,6,7] => [1,4,2,3,5,6,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[2,1,4,3,5,7,6] => [1,3,7,2,4,5,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[2,1,4,3,6,5,7] => [1,3,6,2,4,5,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
[2,1,4,3,6,7,5] => [1,3,5,7,2,4,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[2,1,4,5,3,6,7] => [1,3,5,2,4,6,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[2,1,4,5,3,7,6] => [1,3,4,7,2,5,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[2,1,4,5,6,3,7] => [1,3,4,6,2,5,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[2,3,1,4,6,5,7] => [1,2,6,3,4,5,7] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
[2,3,1,4,6,7,5] => [1,2,5,7,3,4,6] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 1
Description
The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$.
Matching statistic: St000264
(load all 9 compositions to match this statistic)
(load all 9 compositions to match this statistic)
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 49% ●values known / values provided: 49%●distinct values known / distinct values provided: 50%
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 49% ●values known / values provided: 49%●distinct values known / distinct values provided: 50%
Values
[1,3,2,5,4] => [3,5,1,2,4] => [5] => ([],5)
=> ? = 1 + 2
[2,1,4,3,5] => [2,4,1,3,5] => [5] => ([],5)
=> ? = 1 + 2
[1,2,4,3,5,6] => [4,1,2,3,5,6] => [6] => ([],6)
=> ? = 1 + 2
[1,2,4,3,6,5] => [4,6,1,2,3,5] => [6] => ([],6)
=> ? = 1 + 2
[1,3,2,4,6,5] => [3,6,1,2,4,5] => [6] => ([],6)
=> ? = 2 + 2
[1,3,2,5,4,6] => [3,5,1,2,4,6] => [6] => ([],6)
=> ? = 1 + 2
[1,3,2,5,6,4] => [3,5,6,1,2,4] => [6] => ([],6)
=> ? = 1 + 2
[1,3,2,6,4,5] => [6,3,1,2,4,5] => [1,5] => ([(4,5)],6)
=> ? = 1 + 2
[1,3,2,6,5,4] => [6,3,5,1,2,4] => [1,5] => ([(4,5)],6)
=> ? = 1 + 2
[1,3,4,2,6,5] => [3,4,6,1,2,5] => [6] => ([],6)
=> ? = 2 + 2
[1,3,5,2,4,6] => [5,3,1,2,4,6] => [1,5] => ([(4,5)],6)
=> ? = 1 + 2
[1,3,5,2,6,4] => [5,3,6,1,2,4] => [1,5] => ([(4,5)],6)
=> ? = 1 + 2
[1,3,5,4,2,6] => [5,3,4,1,2,6] => [1,5] => ([(4,5)],6)
=> ? = 1 + 2
[1,3,5,4,6,2] => [5,3,4,6,1,2] => [1,5] => ([(4,5)],6)
=> ? = 1 + 2
[1,4,2,3,6,5] => [1,4,6,2,3,5] => [1,5] => ([(4,5)],6)
=> ? = 1 + 2
[1,4,2,5,3,6] => [1,4,5,2,3,6] => [1,5] => ([(4,5)],6)
=> ? = 1 + 2
[1,4,2,6,3,5] => [4,1,6,2,3,5] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 1 + 2
[1,4,2,6,5,3] => [6,1,4,5,2,3] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 1 + 2
[1,4,3,2,6,5] => [4,3,6,1,2,5] => [1,5] => ([(4,5)],6)
=> ? = 1 + 2
[1,4,3,5,2,6] => [4,3,5,1,2,6] => [1,5] => ([(4,5)],6)
=> ? = 1 + 2
[1,4,3,6,2,5] => [4,6,3,1,2,5] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,4,3,6,5,2] => [4,6,3,5,1,2] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
[2,1,3,5,4,6] => [2,5,1,3,4,6] => [6] => ([],6)
=> ? = 2 + 2
[2,1,4,3,5,6] => [2,4,1,3,5,6] => [6] => ([],6)
=> ? = 1 + 2
[2,1,4,3,6,5] => [2,4,6,1,3,5] => [6] => ([],6)
=> ? = 2 + 2
[2,1,4,5,3,6] => [2,4,5,1,3,6] => [6] => ([],6)
=> ? = 2 + 2
[2,1,4,6,3,5] => [6,2,4,1,3,5] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 1 + 2
[2,1,4,6,5,3] => [6,2,4,5,1,3] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 1 + 2
[2,1,5,3,4,6] => [5,2,1,3,4,6] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 1 + 2
[2,1,5,3,6,4] => [5,2,6,1,3,4] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 1 + 2
[2,1,5,4,3,6] => [5,2,4,1,3,6] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 1 + 2
[2,1,5,4,6,3] => [5,2,4,6,1,3] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 1 + 2
[2,3,1,5,4,6] => [2,3,5,1,4,6] => [6] => ([],6)
=> ? = 1 + 2
[2,3,1,5,6,4] => [2,3,5,6,1,4] => [6] => ([],6)
=> ? = 1 + 2
[2,4,1,3,6,5] => [4,2,6,1,3,5] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 1 + 2
[2,4,1,5,3,6] => [4,2,5,1,3,6] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 1 + 2
[2,4,1,6,3,5] => [4,6,2,1,3,5] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
[2,4,1,6,5,3] => [4,6,2,5,1,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
[2,4,3,1,6,5] => [4,2,3,6,1,5] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
[2,4,3,5,1,6] => [4,2,3,5,1,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
[2,4,3,6,1,5] => [4,6,2,3,1,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
[2,4,3,6,5,1] => [4,6,2,3,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
[3,1,2,5,4,6] => [1,3,5,2,4,6] => [1,5] => ([(4,5)],6)
=> ? = 1 + 2
[3,1,2,6,4,5] => [3,1,6,2,4,5] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 1 + 2
[3,1,2,6,5,4] => [6,1,3,5,2,4] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
[3,1,4,2,6,5] => [1,3,4,6,2,5] => [1,5] => ([(4,5)],6)
=> ? = 1 + 2
[3,1,4,6,2,5] => [6,1,3,4,2,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
[3,1,4,6,5,2] => [6,1,3,4,5,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
[3,1,5,2,4,6] => [3,1,5,2,4,6] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 1 + 2
[3,1,5,2,6,4] => [3,1,5,6,2,4] => [2,4] => ([(3,5),(4,5)],6)
=> ? = 1 + 2
[1,5,2,7,3,4,6] => [1,5,2,7,3,4,6] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,2,7,4,3,6] => [1,5,7,4,2,3,6] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,2,7,4,6,3] => [7,5,1,4,6,2,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,2,7,6,3,4] => [7,5,1,2,6,3,4] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,2,7,6,4,3] => [7,5,6,1,4,2,3] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,3,7,2,4,6] => [1,5,7,3,2,4,6] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,3,7,2,6,4] => [7,5,1,3,6,2,4] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,3,7,4,2,6] => [5,3,7,4,1,2,6] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,3,7,4,6,2] => [5,3,7,4,6,1,2] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,3,7,6,2,4] => [7,5,6,1,3,2,4] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,3,7,6,4,2] => [7,3,5,6,4,1,2] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,4,7,2,3,6] => [5,1,7,4,2,3,6] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,4,7,2,6,3] => [5,4,7,1,6,2,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,4,7,3,2,6] => [5,7,4,3,1,2,6] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,4,7,3,6,2] => [5,7,4,3,6,1,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,4,7,6,2,3] => [5,7,4,1,6,2,3] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,5,4,7,6,3,2] => [5,7,4,6,3,1,2] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,1,7,3,5,6] => [7,4,2,1,3,5,6] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,1,7,3,6,5] => [7,4,2,6,1,3,5] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,1,7,5,3,6] => [7,4,2,5,1,3,6] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,1,7,5,6,3] => [7,4,2,5,6,1,3] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,1,7,6,3,5] => [7,4,6,2,1,3,5] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,1,7,6,5,3] => [7,4,6,2,5,1,3] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,3,7,1,5,6] => [7,4,2,3,1,5,6] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,3,7,1,6,5] => [7,4,2,3,6,1,5] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,3,7,5,1,6] => [7,4,2,3,5,1,6] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,3,7,5,6,1] => [7,4,2,3,5,6,1] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,3,7,6,1,5] => [7,4,6,2,3,1,5] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,3,7,6,5,1] => [7,4,6,2,3,5,1] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,6,1,3,7,5] => [6,4,2,7,1,3,5] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,6,1,5,7,3] => [6,4,2,5,7,1,3] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,6,1,7,3,5] => [6,4,7,2,1,3,5] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,6,1,7,5,3] => [6,4,7,2,5,1,3] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,6,3,1,7,5] => [6,4,2,3,7,1,5] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,6,3,5,7,1] => [6,4,2,3,5,7,1] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,6,3,7,1,5] => [6,4,7,2,3,1,5] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,6,3,7,5,1] => [6,4,7,2,3,5,1] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,6,5,1,7,3] => [6,4,5,2,7,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,6,5,3,7,1] => [6,4,5,2,3,7,1] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,6,5,7,1,3] => [6,4,5,7,2,1,3] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,4,6,5,7,3,1] => [6,4,5,7,2,3,1] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,5,1,7,3,4,6] => [5,2,1,7,3,4,6] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,5,1,7,4,3,6] => [5,2,7,4,1,3,6] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,5,1,7,4,6,3] => [5,2,7,4,6,1,3] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,5,1,7,6,3,4] => [7,2,5,1,6,3,4] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,5,1,7,6,4,3] => [7,2,5,6,4,1,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,5,3,7,1,4,6] => [5,2,7,3,1,4,6] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,5,3,7,1,6,4] => [5,2,7,3,6,1,4] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,5,3,7,4,1,6] => [5,2,7,3,4,1,6] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[2,5,3,7,4,6,1] => [5,2,7,3,4,6,1] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Matching statistic: St000968
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St000968: Dyck paths ⟶ ℤResult quality: 31% ●values known / values provided: 31%●distinct values known / distinct values provided: 50%
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St000968: Dyck paths ⟶ ℤResult quality: 31% ●values known / values provided: 31%●distinct values known / distinct values provided: 50%
Values
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 2
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
=> ? = 2
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> ? = 2
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> ? = 2
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2]
=> [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> ? = 2
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> ? = 1
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> ? = 1
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> ? = 1
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> ? = 1
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> ? = 1
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> ? = 1
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
[3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 1
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[3,1,5,4,2,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[3,1,5,4,6,2] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
[3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
[3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 1
[3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1
[3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1
[3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[3,2,5,1,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2,1]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,2,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,2,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,5,3,7,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,2,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 2
[1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,1,1]
=> [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 2
[1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 1
[3,1,4,7,2,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,2,6,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,5,2,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,5,6,2] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,6,2,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,6,5,2] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,5,7,2,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,2,6,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,4,2,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,4,6,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,6,2,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,6,4,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,4,7,1,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,1,6,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,5,1,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,5,6,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,6,1,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,6,5,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,5,7,1,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,1,6,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,4,1,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,4,6,1] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,6,1,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,6,4,1] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,5,1,7,2,4,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[3,5,1,7,2,6,4] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[3,5,1,7,4,2,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[3,5,1,7,4,6,2] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
Description
We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n−1}]$ by adding $c_0$ to $c_{n−1}$. Then we calculate the dominant dimension of that CNakayama algebra.
Matching statistic: St001256
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001256: Dyck paths ⟶ ℤResult quality: 31% ●values known / values provided: 31%●distinct values known / distinct values provided: 50%
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001256: Dyck paths ⟶ ℤResult quality: 31% ●values known / values provided: 31%●distinct values known / distinct values provided: 50%
Values
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 2
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
=> ? = 2
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> ? = 2
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> ? = 2
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2]
=> [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> ? = 2
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> ? = 1
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> ? = 1
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> ? = 1
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> ? = 1
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> ? = 1
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> ? = 1
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
[3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 1
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[3,1,5,4,2,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[3,1,5,4,6,2] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
[3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
[3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 1
[3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1
[3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1
[3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[3,2,5,1,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2,1]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,2,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,2,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,5,3,7,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,2,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 2
[1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,1,1]
=> [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 2
[1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 1
[3,1,4,7,2,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,2,6,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,5,2,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,5,6,2] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,6,2,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,6,5,2] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,5,7,2,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,2,6,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,4,2,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,4,6,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,6,2,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,6,4,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,4,7,1,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,1,6,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,5,1,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,5,6,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,6,1,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,6,5,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,5,7,1,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,1,6,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,4,1,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,4,6,1] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,6,1,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,6,4,1] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,5,1,7,2,4,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[3,5,1,7,2,6,4] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[3,5,1,7,4,2,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[3,5,1,7,4,6,2] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
Description
Number of simple reflexive modules that are 2-stable reflexive.
See Definition 3.1. in the reference for the definition of 2-stable reflexive.
Matching statistic: St001493
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001493: Dyck paths ⟶ ℤResult quality: 31% ●values known / values provided: 31%●distinct values known / distinct values provided: 50%
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001493: Dyck paths ⟶ ℤResult quality: 31% ●values known / values provided: 31%●distinct values known / distinct values provided: 50%
Values
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 2
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
=> ? = 2
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> ? = 2
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> ? = 2
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2]
=> [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> ? = 2
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> ? = 1
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> ? = 1
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> ? = 1
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> ? = 1
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> ? = 1
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> ? = 1
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
[3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 1
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[3,1,5,4,2,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[3,1,5,4,6,2] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
[3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
[3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 1
[3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1
[3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1
[3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[3,2,5,1,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 1
[1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2,1]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,2,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,2,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1
[1,2,4,5,3,7,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,2,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 2
[1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,1,1]
=> [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 2
[1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 1
[3,1,4,7,2,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,2,6,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,5,2,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,5,6,2] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,6,2,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,4,7,6,5,2] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,1,5,7,2,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,2,6,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,4,2,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,4,6,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,6,2,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,1,5,7,6,4,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,4,7,1,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,1,6,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,5,1,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,5,6,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,6,1,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,4,7,6,5,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[3,2,5,7,1,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,1,6,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,4,1,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,4,6,1] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,6,1,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,2,5,7,6,4,1] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1
[3,5,1,7,2,4,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[3,5,1,7,2,6,4] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[3,5,1,7,4,2,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
[3,5,1,7,4,6,2] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 1
Description
The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra.
Matching statistic: St001221
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001221: Dyck paths ⟶ ℤResult quality: 31% ●values known / values provided: 31%●distinct values known / distinct values provided: 50%
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001221: Dyck paths ⟶ ℤResult quality: 31% ●values known / values provided: 31%●distinct values known / distinct values provided: 50%
Values
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 0 = 1 - 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 0 = 1 - 1
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> ? = 1 - 1
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> ? = 1 - 1
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 2 - 1
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1 - 1
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1 - 1
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1 - 1
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 1 - 1
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
=> ? = 2 - 1
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1 - 1
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1 - 1
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1 - 1
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 1 - 1
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1 - 1
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1 - 1
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1 - 1
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1 - 1
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1 - 1
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1 - 1
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1 - 1
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> ? = 1 - 1
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> ? = 2 - 1
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> ? = 1 - 1
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> ? = 2 - 1
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2]
=> [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> ? = 2 - 1
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 1 - 1
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 1 - 1
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1 - 1
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1 - 1
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1 - 1
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1 - 1
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> ? = 1 - 1
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> ? = 1 - 1
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> ? = 1 - 1
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> ? = 1 - 1
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 0 = 1 - 1
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 0 = 1 - 1
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> ? = 1 - 1
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> ? = 1 - 1
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 0 = 1 - 1
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 0 = 1 - 1
[3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1 - 1
[3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 0 = 1 - 1
[3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 0 = 1 - 1
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1 - 1
[3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,5,4,2,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1 - 1
[3,1,5,4,6,2] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1 - 1
[3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 0 = 1 - 1
[3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> 0 = 1 - 1
[3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1 - 1
[3,2,5,1,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1 - 1
[3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 0 = 1 - 1
[1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ? = 1 - 1
[1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ? = 1 - 1
[1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2,1]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1 - 1
[1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1 - 1
[1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,2,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1 - 1
[1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,2,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1 - 1
[1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 1 - 1
[1,2,4,5,3,7,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,2,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ? = 2 - 1
[1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,1,1]
=> [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 2 - 1
[1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 1 - 1
[3,1,4,7,2,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,4,7,2,6,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,4,7,5,2,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,4,7,5,6,2] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,4,7,6,2,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,4,7,6,5,2] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,5,7,2,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,5,7,2,6,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,5,7,4,2,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,5,7,4,6,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,5,7,6,2,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,1,5,7,6,4,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,4,7,1,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,4,7,1,6,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,4,7,5,1,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,4,7,5,6,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,4,7,6,1,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,4,7,6,5,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,5,7,1,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,5,7,1,6,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,5,7,4,1,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,5,7,4,6,1] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,5,7,6,1,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,2,5,7,6,4,1] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 1 - 1
[3,5,1,7,2,4,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 0 = 1 - 1
[3,5,1,7,2,6,4] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 0 = 1 - 1
[3,5,1,7,4,2,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 0 = 1 - 1
[3,5,1,7,4,6,2] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 0 = 1 - 1
Description
The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module.
The following 135 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001645The pebbling number of a connected graph. St000455The second largest eigenvalue of a graph if it is integral. St000007The number of saliances of the permutation. St000256The number of parts from which one can substract 2 and still get an integer partition. St000781The number of proper colouring schemes of a Ferrers diagram. St001568The smallest positive integer that does not appear twice in the partition. St000143The largest repeated part of a partition. St000454The largest eigenvalue of a graph if it is integral. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001695The natural comajor index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001699The major index of a standard tableau minus the weighted size of its shape. St001712The number of natural descents of a standard Young tableau. St000744The length of the path to the largest entry in a standard Young tableau. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St000022The number of fixed points of a permutation. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St000153The number of adjacent cycles of a permutation. St000402Half the size of the symmetry class of a permutation. St000546The number of global descents of a permutation. St000036The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000312The number of leaves in a graph. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000260The radius of a connected graph. St000259The diameter of a connected graph. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000862The number of parts of the shifted shape of a permutation. St001198The 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 $eA$. St001206The 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 $eA$. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001613The binary logarithm of the size of the center of a lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001820The size of the image of the pop stack sorting operator. St001881The number of factors of a lattice as a Cartesian product of lattices. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St001616The number of neutral elements in a lattice. St001720The minimal length of a chain of small intervals in a lattice. St001846The number of elements which do not have a complement in the lattice. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000124The cardinality of the preimage of the Simion-Schmidt map. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001618The cardinality of the Frattini sublattice of a lattice. St001845The number of join irreducibles minus the rank of a lattice. St001619The number of non-isomorphic sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St001681The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. St001833The number of linear intervals in a lattice. St001677The number of non-degenerate subsets of a lattice whose meet is the bottom element. St001620The number of sublattices of a lattice. St001679The number of subsets of a lattice whose meet is the bottom element. St000065The number of entries equal to -1 in an alternating sign matrix. St001570The minimal number of edges to add to make a graph Hamiltonian. St001947The number of ties in a parking function. St001060The distinguishing index of a graph. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001564The value of the forgotten symmetric functions when all variables set to 1. St001563The value of the power-sum symmetric function evaluated at 1. St001562The value of the complete homogeneous symmetric function evaluated at 1. St001607The number of coloured graphs such that the multiplicities of colours are given by a partition. St001330The hat guessing number of a graph. St000422The energy of a graph, if it is integral. St001434The number of negative sum pairs of a signed permutation. St001964The interval resolution global dimension of a poset. St000408The number of occurrences of the pattern 4231 in a permutation. St000842The breadth of a permutation. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St001322The size of a minimal independent dominating set in a graph. St001333The cardinality of a minimal edge-isolating set of a graph. St001339The irredundance number of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001363The Euler characteristic of a graph according to Knill. St001393The induced matching number of a graph. St001496The number of graphs with the same Laplacian spectrum as the given graph. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St000359The number of occurrences of the pattern 23-1. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001261The Castelnuovo-Mumford regularity of a graph. St001325The minimal number of occurrences of the comparability-pattern in a linear ordering of the vertices of the graph. St001367The smallest number which does not occur as degree of a vertex in a graph. St000647The number of big descents of a permutation. St000662The staircase size of the code of a permutation. St001331The size of the minimal feedback vertex set. St001963The tree-depth of a graph. St000527The width of the poset. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St000741The Colin de Verdière graph invariant. St000879The number of long braid edges in the graph of braid moves of a permutation. St001208The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$. St001520The number of strict 3-descents. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000929The constant term of the character polynomial of an integer partition. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001371The length of the longest Yamanouchi prefix of a binary word. St001556The number of inversions of the third entry of a permutation. St001730The number of times the path corresponding to a binary word crosses the base line. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001948The number of augmented double ascents of a permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St000735The last entry on the main diagonal of a standard tableau. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St000044The number of vertices of the unicellular map given by a perfect matching. St000017The number of inversions of a standard tableau. St001721The degree of a binary word. St000016The number of attacking pairs of a standard tableau. St000958The number of Bruhat factorizations of a permutation. St001260The permanent of an alternating sign matrix. St000352The Elizalde-Pak rank of a permutation. St000648The number of 2-excedences of a permutation. St000834The number of right outer peaks of a permutation. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St000508Eigenvalues of the random-to-random operator acting on a simple module. St001413Half the length of the longest even length palindromic prefix of a binary word. St001557The number of inversions of the second entry of a permutation. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001875The number of simple modules with projective dimension at most 1. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
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!