Identifier
Mp00058:
Perfect matchings
—to permutation⟶
Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
Mp00065: Permutations —permutation poset⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
Images
[(1,2)] => [2,1] => ([],2) => ([],2)
[(1,2),(3,4)] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4)
[(1,3),(2,4)] => [3,4,1,2] => ([(0,3),(1,2)],4) => ([(0,3),(1,2)],4)
[(1,4),(2,3)] => [4,3,2,1] => ([],4) => ([],4)
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6)
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(2,4),(2,5),(3,4),(3,5)],6)
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6)
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,4),(0,5),(1,2),(1,3)],6)
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => ([(0,5),(1,4),(4,2),(5,3)],6)
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) => ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => ([(0,4),(0,5),(1,2),(1,3)],6) => ([(0,5),(1,5),(2,4),(3,4)],6)
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6)
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => ([],6) => ([],6)
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => ([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8) => ([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => ([(0,3),(1,2),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8) => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(6,5),(7,4),(7,5)],8)
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8) => ([(0,6),(0,7),(1,6),(1,7),(6,2),(6,3),(6,4),(6,5),(7,2),(7,3),(7,4),(7,5)],8)
[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8) => ([(0,6),(0,7),(1,6),(1,7),(6,3),(6,4),(6,5),(7,2),(7,4),(7,5)],8)
[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,2),(6,3),(7,2),(7,3)],8)
[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => ([(0,7),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(6,4),(6,5),(7,4),(7,5)],8)
[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => ([(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8) => ([(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => ([(2,5),(3,4),(4,6),(4,7),(5,6),(5,7)],8) => ([(2,6),(2,7),(3,6),(3,7),(6,5),(7,4)],8)
[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => ([(0,7),(1,6),(2,5),(3,4),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(6,3),(7,2)],8)
[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,3),(7,2)],8)
[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,6),(0,7),(1,6),(1,7),(6,4),(6,5),(7,2),(7,3)],8)
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8) => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8)
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => ([(0,3),(0,7),(1,2),(1,6),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4)],8)
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(6,3),(7,2)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(6,3),(7,2)],8)
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(4,3),(5,3),(6,2),(7,2)],8)
[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,3),(7,2)],8)
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)
[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7)],8)
[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7)],8)
[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => ([(0,7),(1,7),(2,6),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7)],8)
[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(4,6),(5,7)],8) => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(4,2),(5,3)],8)
[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6),(4,7),(5,6)],8) => ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,5),(3,4)],8)
[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => ([(0,3),(0,5),(1,2),(1,4),(2,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(2,4),(3,5),(6,4),(7,5)],8)
[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,2),(6,3),(7,2),(7,3)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => ([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(6,4),(6,5),(7,4),(7,5)],8) => ([(0,7),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => ([(0,3),(0,5),(1,2),(1,4),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,7),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,7)],8)
[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7)],8) => ([(0,7),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6)],8) => ([(0,5),(1,4),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7)],8)
[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8)
[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => ([(4,6),(4,7),(5,6),(5,7)],8) => ([(4,6),(4,7),(5,6),(5,7)],8)
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => ([(4,7),(5,6)],8) => ([(4,7),(5,6)],8)
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => ([(0,7),(1,6),(2,5),(3,4)],8) => ([(0,7),(1,6),(2,5),(3,4)],8)
[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => ([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8) => ([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8)
[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => ([(0,5),(0,7),(1,4),(1,6),(6,2),(7,3)],8) => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8)
[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => ([(0,3),(0,5),(0,7),(1,2),(1,4),(1,6),(4,7),(5,6)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,6),(5,7)],8)
[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(6,3),(7,2)],8) => ([(0,7),(1,6),(2,5),(3,4),(4,6),(4,7),(5,6),(5,7)],8)
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,3),(7,2)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(4,6),(4,7),(5,6),(5,7)],8)
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(4,3),(5,3),(6,2),(7,2)],8) => ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => ([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(2,4),(3,5),(6,4),(7,5)],8) => ([(0,3),(0,5),(1,2),(1,4),(2,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,7),(3,7),(4,6),(5,6)],8) => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,7),(3,7),(4,6),(5,6)],8)
[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,7),(5,7)],8) => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,7),(5,7)],8)
[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8) => ([(0,5),(0,7),(1,4),(1,6),(6,2),(7,3)],8)
[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4)],8)
[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => ([(2,7),(3,7),(4,6),(5,6)],8) => ([(2,6),(2,7),(3,4),(3,5)],8)
[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => ([(2,5),(3,4),(4,6),(5,7)],8) => ([(2,5),(3,4),(4,6),(5,7)],8)
[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8) => ([(0,5),(0,7),(1,4),(1,6),(6,2),(7,3)],8)
[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => ([(0,6),(1,6),(2,7),(3,7),(6,5),(7,4)],8) => ([(0,7),(1,6),(6,2),(6,3),(7,4),(7,5)],8)
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => ([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8) => ([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => ([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8) => ([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8)
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => ([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8) => ([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8)
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8) => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8)
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4)],8) => ([(0,3),(0,7),(1,2),(1,6),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8)
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => ([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8) => ([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8)
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => ([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8) => ([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8)
[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => ([(0,5),(0,7),(1,5),(1,7),(2,4),(2,6),(3,4),(3,6),(4,7),(5,6)],8) => ([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,6),(2,7),(3,4),(3,5)],8)
[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => ([(0,5),(1,4),(2,4),(2,7),(3,5),(3,6),(4,6),(5,7)],8) => ([(0,5),(0,7),(1,4),(1,6),(4,2),(4,7),(5,3),(5,6)],8)
[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,6),(5,7)],8) => ([(0,3),(0,5),(0,7),(1,2),(1,4),(1,6),(4,7),(5,6)],8)
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => ([(2,5),(2,7),(3,4),(3,6),(4,7),(5,6)],8) => ([(2,5),(2,7),(3,4),(3,6),(4,7),(5,6)],8)
[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => ([(2,6),(2,7),(3,6),(3,7),(6,5),(7,4)],8) => ([(2,5),(3,4),(4,6),(4,7),(5,6),(5,7)],8)
[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => ([(0,7),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,7)],8) => ([(0,3),(0,5),(1,2),(1,4),(4,6),(4,7),(5,6),(5,7)],8)
[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(6,4),(7,5)],8) => ([(0,5),(1,4),(4,2),(4,6),(4,7),(5,3),(5,6),(5,7)],8)
[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6),(6,5),(7,4)],8) => ([(0,3),(0,7),(1,2),(1,6),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6)],8)
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,5),(7,4)],8) => ([(0,3),(1,2),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => ([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8) => ([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8)
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(6,5),(7,4),(7,5)],8) => ([(0,3),(1,2),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => ([(0,6),(0,7),(1,6),(1,7),(6,2),(6,3),(6,4),(6,5),(7,2),(7,3),(7,4),(7,5)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => ([(0,3),(1,2),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,5),(7,4)],8)
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7)],8)
[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => ([(0,7),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7)],8)
[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7)],8) => ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => ([(0,5),(1,4),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7)],8) => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6)],8)
[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => ([(0,5),(0,7),(1,4),(1,6),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7)],8) => ([(0,5),(0,7),(1,4),(1,6),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7)],8)
[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7)],8) => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => ([(0,5),(1,4),(4,2),(4,6),(4,7),(5,3),(5,6),(5,7)],8) => ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(6,4),(7,5)],8)
>>> Load all 135 entries. <<<Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
Map
dual poset
Description
The dual of a poset.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.
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