Identifier
Mp00201:
Dyck paths
—Ringel⟶
Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
Mp00065: Permutations —permutation poset⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
Images
[1,0] => [2,1] => ([],2) => ([],2)
[1,0,1,0] => [3,1,2] => ([(1,2)],3) => ([(1,2)],3)
[1,1,0,0] => [2,3,1] => ([(1,2)],3) => ([(1,2)],3)
[1,0,1,0,1,0] => [4,1,2,3] => ([(1,2),(2,3)],4) => ([(1,2),(2,3)],4)
[1,0,1,1,0,0] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4) => ([(0,3),(1,2),(1,3)],4)
[1,1,0,0,1,0] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => ([(0,3),(1,2),(1,3)],4)
[1,1,0,1,0,0] => [4,3,1,2] => ([(2,3)],4) => ([(2,3)],4)
[1,1,1,0,0,0] => [2,3,4,1] => ([(1,2),(2,3)],4) => ([(1,2),(2,3)],4)
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => ([(1,4),(3,2),(4,3)],5)
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => ([(0,4),(1,2),(2,3),(2,4)],5) => ([(0,4),(1,2),(1,4),(4,3)],5)
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => ([(1,3),(1,4),(4,2)],5) => ([(1,4),(2,3),(3,4)],5)
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5) => ([(0,4),(1,2),(2,3),(2,4)],5)
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => ([(0,4),(1,2),(1,4),(4,3)],5) => ([(0,4),(1,2),(2,3),(2,4)],5)
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => ([(1,3),(1,4),(4,2)],5)
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => ([(2,3),(3,4)],5)
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => ([(0,4),(1,4),(2,3),(2,4)],5) => ([(0,4),(1,2),(1,3),(1,4)],5)
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => ([(0,4),(1,2),(2,3),(2,4)],5) => ([(0,4),(1,2),(1,4),(4,3)],5)
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(1,4)],5) => ([(0,4),(1,4),(2,3),(2,4)],5)
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5)
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5) => ([(1,4),(3,2),(4,3)],5)
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => ([(1,5),(3,4),(4,2),(5,3)],6)
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => ([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => ([(1,5),(4,3),(5,2),(5,4)],6) => ([(1,5),(2,3),(3,5),(5,4)],6)
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => ([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => ([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => ([(1,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => ([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6) => ([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => ([(1,4),(1,5),(4,3),(5,2)],6) => ([(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => ([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => ([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => ([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => ([(1,5),(4,3),(5,2),(5,4)],6)
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => ([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(1,3),(1,5),(4,2),(5,4)],6)
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => ([(0,5),(1,3),(4,2),(5,4)],6)
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => ([(0,5),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,5),(1,2),(1,3),(1,5),(5,4)],6)
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => ([(1,4),(1,5),(2,3),(2,4),(3,5)],6) => ([(1,4),(1,5),(2,3),(2,4),(3,5)],6)
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => ([(1,5),(2,3),(2,5),(3,4)],6) => ([(1,4),(2,3),(2,5),(4,5)],6)
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,5),(5,4)],6) => ([(0,5),(1,4),(4,2),(4,3),(4,5)],6)
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => ([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => ([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => ([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => ([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6)
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => ([(0,5),(1,2),(1,3),(1,5),(5,4)],6) => ([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6) => ([(1,4),(1,5),(4,3),(5,2)],6)
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => ([(1,4),(2,3),(2,5),(4,5)],6) => ([(1,5),(2,3),(2,5),(3,4)],6)
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => ([(3,4),(4,5)],6)
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => ([(0,5),(1,4),(2,3),(2,5),(4,5)],6) => ([(0,5),(1,3),(1,4),(1,5),(4,2)],6)
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => ([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => ([(0,5),(1,4),(4,2),(4,3),(4,5)],6) => ([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => ([(0,5),(1,3),(1,4),(1,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,5),(4,5)],6)
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => ([(1,3),(2,4),(4,5)],6) => ([(1,3),(2,4),(4,5)],6)
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6) => ([(1,5),(3,4),(4,2),(5,3)],6)
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => ([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7) => ([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => ([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7) => ([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7)
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => ([(1,5),(4,3),(5,6),(6,2),(6,4)],7) => ([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => ([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7) => ([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => ([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7) => ([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7)
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => ([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7) => ([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => ([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7) => ([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => ([(1,6),(4,5),(5,3),(6,2),(6,4)],7) => ([(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => ([(0,6),(1,5),(3,6),(4,2),(4,6),(5,3),(5,4)],7) => ([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7)
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => ([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7) => ([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7)
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => ([(0,3),(1,4),(1,5),(1,6),(2,6),(3,2),(3,4),(3,5)],7) => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7)
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => ([(1,6),(4,3),(5,2),(6,4),(6,5)],7) => ([(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => ([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7) => ([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7)
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => ([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7) => ([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7)
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7) => ([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7)
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => ([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(5,2)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(5,4)],7)
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => ([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7) => ([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7)
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => ([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7) => ([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => ([(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) => ([(0,5),(0,6),(1,2),(1,5),(1,6),(3,4),(5,3),(6,4)],7)
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => ([(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7) => ([(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => ([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7) => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => ([(0,6),(1,3),(1,4),(3,6),(4,5),(5,2),(5,6)],7) => ([(0,6),(1,2),(1,4),(1,6),(3,5),(4,5),(6,3)],7)
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => ([(0,5),(0,6),(1,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7) => ([(0,2),(0,4),(0,6),(1,4),(1,5),(1,6),(2,5),(5,3),(6,3)],7)
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => ([(1,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7) => ([(1,4),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => ([(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7) => ([(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => ([(0,6),(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7) => ([(0,6),(1,4),(3,5),(4,2),(4,3),(4,6),(6,5)],7)
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => ([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) => ([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7)
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => ([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7) => ([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7)
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => ([(0,2),(0,4),(0,6),(1,4),(1,5),(1,6),(2,5),(5,3),(6,3)],7) => ([(0,5),(0,6),(1,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => ([(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(3,4),(4,2)],7) => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6),(4,5)],7)
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => ([(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7) => ([(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7)
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => ([(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7) => ([(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => ([(1,3),(1,4),(1,6),(5,2),(6,5)],7) => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => ([(0,6),(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7) => ([(0,6),(1,2),(1,4),(1,6),(3,5),(4,3),(6,5)],7)
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Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation π of length n, this poset has vertices
{(i,π(i)) : 1≤i≤n}
and the cover relation is given by (w,x)≤(y,z) if w≤y and x≤z.
For example, the permutation [3,1,5,4,2] is mapped to the poset with cover relations
{(2,1)≺(5,2), (2,1)≺(4,4), (2,1)≺(3,5), (1,3)≺(4,4), (1,3)≺(3,5)}.
For a permutation π of length n, this poset has vertices
{(i,π(i)) : 1≤i≤n}
and the cover relation is given by (w,x)≤(y,z) if w≤y and x≤z.
For example, the permutation [3,1,5,4,2] is mapped to the poset with cover relations
{(2,1)≺(5,2), (2,1)≺(4,4), (2,1)≺(3,5), (1,3)≺(4,4), (1,3)≺(3,5)}.
Map
dual poset
Description
The dual of a poset.
The dual (or opposite) of a poset (P,≤) is the poset (Pd,≤d) with x≤dy if y≤x.
The dual (or opposite) of a poset (P,≤) is the poset (Pd,≤d) with x≤dy if y≤x.
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