Identifier
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Images
[(1,2)] => [2,1] => [1,2] => ([(0,1)],2)
[(1,2),(3,4)] => [2,1,4,3] => [3,4,1,2] => ([(0,3),(1,2)],4)
[(1,3),(2,4)] => [3,4,1,2] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
[(1,4),(2,3)] => [4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [5,6,2,1,4,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3)],6)
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6)
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [4,1,6,2,3,5] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [1,3,2,5,4,6] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [3,1,2,6,4,5] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [4,2,6,1,5,3] => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6)
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [4,3,6,5,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,3)],6)
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [2,4,5,1,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [2,3,1,5,6,4] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [2,1,3,4,6,5] => ([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [7,8,5,6,3,4,1,2] => ([(0,7),(1,6),(2,5),(3,4)],8)
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [7,8,5,6,2,1,4,3] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8)
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [7,8,5,6,1,2,3,4] => ([(0,5),(1,4),(2,7),(6,3),(7,6)],8)
[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => [7,8,4,1,6,2,3,5] => ([(0,6),(0,7),(1,3),(2,4),(2,6),(4,5),(5,7)],8)
[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [7,8,1,4,5,2,3,6] => ([(0,4),(1,5),(1,6),(2,7),(3,7),(5,3),(6,2)],8)
[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => [6,1,8,4,5,2,3,7] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(2,7),(3,7),(4,3),(5,2)],8)
[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [1,6,7,4,5,2,3,8] => ([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,3),(5,2),(6,1)],8)
[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => [1,6,7,3,2,5,4,8] => ([(0,2),(0,3),(0,4),(1,7),(2,5),(2,6),(3,5),(3,6),(4,1),(5,7),(6,7)],8)
[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => [6,1,8,3,2,5,4,7] => ([(0,6),(0,7),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,7),(5,7)],8)
[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => [7,8,1,3,2,5,4,6] => ([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7)],8)
[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => [7,8,3,1,2,6,4,5] => ([(0,6),(0,7),(1,3),(2,5),(5,6),(5,7),(7,4)],8)
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [7,8,3,2,1,6,5,4] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4)],8)
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [7,8,4,2,6,1,5,3] => ([(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4)],8)
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [7,8,4,3,6,5,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8)
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [7,8,3,4,5,6,1,2] => ([(0,5),(1,4),(2,7),(6,3),(7,6)],8)
[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => [7,8,2,4,5,1,6,3] => ([(0,6),(0,7),(1,3),(2,4),(2,6),(4,5),(5,7)],8)
[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => [7,8,2,3,1,5,6,4] => ([(0,6),(0,7),(1,3),(2,5),(5,6),(5,7),(7,4)],8)
[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => [7,8,2,1,3,4,6,5] => ([(0,7),(1,7),(2,5),(6,3),(6,4),(7,6)],8)
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [7,8,1,2,3,4,5,6] => ([(0,7),(1,3),(4,6),(5,4),(6,2),(7,5)],8)
[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => [6,1,8,2,3,4,5,7] => ([(0,6),(0,7),(1,5),(1,7),(2,6),(3,4),(4,2),(5,3)],8)
[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [1,6,7,2,3,4,5,8] => ([(0,5),(0,6),(1,7),(2,7),(3,4),(4,2),(5,3),(6,1)],8)
[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => [1,5,2,7,3,4,6,8] => ([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(4,3),(4,6),(5,7),(6,7)],8)
[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => [5,1,2,8,3,4,6,7] => ([(0,6),(0,7),(1,5),(3,7),(4,3),(5,4),(5,6),(7,2)],8)
[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => [5,2,1,8,3,4,7,6] => ([(0,4),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(4,3)],8)
[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => [6,2,8,1,3,4,7,5] => ([(0,6),(1,5),(1,6),(2,5),(2,7),(3,4),(3,7),(6,3)],8)
[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => [6,2,8,3,1,5,7,4] => ([(0,3),(0,5),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(7,4)],8)
[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => [6,2,8,4,5,1,7,3] => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8)
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [6,3,8,4,5,7,1,2] => ([(0,6),(0,7),(1,3),(2,4),(2,6),(4,5),(5,7)],8)
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [3,6,7,4,5,8,1,2] => ([(0,4),(1,5),(1,6),(2,7),(3,7),(5,3),(6,2)],8)
[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => [2,6,7,4,5,1,8,3] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(2,7),(3,7),(4,3),(5,2)],8)
[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => [2,6,7,3,1,5,8,4] => ([(0,6),(0,7),(1,3),(1,4),(2,5),(3,6),(3,7),(4,2),(7,5)],8)
[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => [2,6,7,1,3,4,8,5] => ([(0,7),(1,4),(1,7),(3,6),(4,3),(5,2),(5,6),(7,5)],8)
[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => [2,5,1,7,3,4,8,6] => ([(0,3),(0,6),(1,6),(1,7),(2,4),(2,5),(3,4),(3,7),(6,2),(7,5)],8)
[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => [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)
[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [1,2,5,6,3,4,7,8] => ([(0,6),(1,7),(2,7),(4,2),(5,1),(6,4),(6,5),(7,3)],8)
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [1,2,4,3,6,5,7,8] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(5,7),(6,7),(7,1)],8)
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => [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)
[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => [2,4,1,3,7,5,8,6] => ([(0,7),(1,3),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5),(7,6)],8)
[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => [2,4,3,1,7,6,8,5] => ([(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => [2,5,3,7,1,6,8,4] => ([(0,2),(0,3),(1,4),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(6,5),(7,5)],8)
[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => [2,5,4,7,6,1,8,3] => ([(0,6),(0,7),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,7),(5,7)],8)
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [3,5,4,7,6,8,1,2] => ([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7)],8)
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [5,3,4,8,6,7,1,2] => ([(0,6),(0,7),(1,3),(2,5),(5,6),(5,7),(7,4)],8)
[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => [5,2,4,8,6,1,7,3] => ([(0,3),(0,5),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(7,4)],8)
[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => [5,2,3,8,1,6,7,4] => ([(0,6),(0,7),(1,5),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8)
[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => [4,2,3,1,8,6,7,5] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8)
[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => [4,2,1,3,8,5,7,6] => ([(0,6),(0,7),(1,5),(2,5),(5,6),(5,7),(7,3),(7,4)],8)
[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => [4,1,2,3,8,5,6,7] => ([(0,6),(0,7),(1,4),(3,6),(3,7),(4,3),(5,2),(7,5)],8)
[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => [1,4,2,3,7,5,6,8] => ([(0,3),(0,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(5,6),(7,1)],8)
[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => [1,4,3,2,7,6,5,8] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => [4,1,3,2,8,6,5,7] => ([(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => [4,3,1,2,8,7,5,6] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8)
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [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)
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [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)
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [5,4,2,8,7,1,6,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [5,4,3,8,7,6,1,2] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4)],8)
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [6,4,8,3,7,5,1,2] => ([(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4)],8)
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [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)
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [6,3,8,2,1,7,5,4] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => [6,3,8,1,2,7,4,5] => ([(0,5),(0,7),(1,5),(1,6),(1,7),(2,4),(4,6),(4,7),(6,3)],8)
[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => [5,3,1,8,2,7,4,6] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(3,5),(3,7),(5,4)],8)
[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => [5,1,3,8,2,6,4,7] => ([(0,2),(0,3),(1,4),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(6,5),(7,5)],8)
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [1,5,3,7,2,6,4,8] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => [1,5,4,7,6,2,3,8] => ([(0,2),(0,3),(0,4),(1,7),(2,5),(2,6),(3,5),(3,6),(4,1),(5,7),(6,7)],8)
[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => [5,1,4,8,6,2,3,7] => ([(0,6),(0,7),(1,3),(1,4),(2,5),(3,6),(3,7),(4,2),(7,5)],8)
[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => [5,4,1,8,7,2,3,6] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8)
[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => [6,4,8,1,7,2,3,5] => ([(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,7),(3,4),(4,6)],8)
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [6,5,8,7,1,2,3,4] => ([(0,3),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4)],8)
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [6,5,8,7,2,1,4,3] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7)],8)
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [6,5,8,7,3,4,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8)
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [5,6,7,8,3,4,1,2] => ([(0,5),(1,4),(2,7),(6,3),(7,6)],8)
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => [5,6,7,8,2,1,4,3] => ([(0,3),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4)],8)
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [5,6,7,8,1,2,3,4] => ([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => [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)
[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => [4,5,1,7,8,2,3,6] => ([(0,4),(1,5),(1,7),(3,6),(4,6),(4,7),(5,3),(7,2)],8)
[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => [4,1,5,6,8,2,3,7] => ([(0,7),(1,4),(1,7),(3,6),(4,3),(5,2),(5,6),(7,5)],8)
[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [1,4,5,6,7,2,3,8] => ([(0,5),(0,6),(1,7),(2,7),(3,4),(4,2),(5,3),(6,1)],8)
[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => [1,3,5,6,2,7,4,8] => ([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(4,3),(4,6),(5,7),(6,7)],8)
[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => [3,1,5,6,2,8,4,7] => ([(0,3),(0,6),(1,6),(1,7),(2,4),(2,5),(3,4),(3,7),(6,2),(7,5)],8)
[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => [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)
[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => [3,6,7,1,2,8,4,5] => ([(0,4),(1,5),(1,7),(3,6),(4,6),(4,7),(5,3),(7,2)],8)
[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => [3,6,7,2,1,8,5,4] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8)
>>> Load all 313 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => [4,6,7,2,8,1,5,3] => ([(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,7),(3,4),(4,6)],8)
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => [4,6,7,3,8,5,1,2] => ([(0,6),(0,7),(1,3),(2,4),(2,6),(4,5),(5,7)],8)
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => [4,5,3,7,8,6,1,2] => ([(0,6),(0,7),(1,3),(2,5),(5,6),(5,7),(7,4)],8)
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,8,7,2,5,4] => [4,5,2,7,8,1,6,3] => ([(0,5),(0,7),(1,5),(1,6),(1,7),(2,4),(4,6),(4,7),(6,3)],8)
[(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => [3,5,2,7,1,8,6,4] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(3,5),(3,7),(5,4)],8)
[(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => [3,4,2,1,7,8,6,5] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8)
[(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => [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)
[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => [3,1,4,2,6,8,5,7] => ([(0,7),(1,3),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5),(7,6)],8)
[(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => [1,3,4,2,6,7,5,8] => ([(0,3),(0,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(5,6),(7,1)],8)
[(1,8),(2,6),(3,7),(4,5)] => [8,6,7,5,4,2,3,1] => [1,3,2,4,5,7,6,8] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
[(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => [3,1,2,4,5,8,6,7] => ([(0,7),(1,4),(4,7),(5,3),(6,2),(6,5),(7,6)],8)
[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => [3,2,1,4,5,8,7,6] => ([(0,7),(1,7),(2,7),(6,3),(6,4),(6,5),(7,6)],8)
[(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => [3,2,4,1,6,8,7,5] => ([(0,6),(0,7),(1,5),(2,5),(5,6),(5,7),(7,3),(7,4)],8)
[(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => [3,2,5,6,1,8,7,4] => ([(0,4),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(4,3)],8)
[(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => [4,2,5,6,8,1,7,3] => ([(0,6),(1,5),(1,6),(2,5),(2,7),(3,4),(3,7),(6,3)],8)
[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => [4,3,5,6,8,7,1,2] => ([(0,7),(1,7),(2,5),(6,3),(6,4),(7,6)],8)
[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [3,4,5,6,7,8,1,2] => ([(0,7),(1,3),(4,6),(5,4),(6,2),(7,5)],8)
[(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => [2,4,5,6,7,1,8,3] => ([(0,6),(0,7),(1,5),(1,7),(2,6),(3,4),(4,2),(5,3)],8)
[(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => [2,3,5,6,1,7,8,4] => ([(0,6),(0,7),(1,5),(3,7),(4,3),(5,4),(5,6),(7,2)],8)
[(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => [2,3,4,1,6,7,8,5] => ([(0,6),(0,7),(1,4),(3,6),(3,7),(4,3),(5,2),(7,5)],8)
[(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => [2,3,1,4,5,7,8,6] => ([(0,7),(1,4),(4,7),(5,3),(6,2),(6,5),(7,6)],8)
[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => [2,1,3,4,5,6,8,7] => ([(0,7),(1,7),(4,6),(5,4),(6,2),(6,3),(7,5)],8)
[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [9,10,7,8,5,6,3,4,1,2] => ([(0,9),(1,8),(2,7),(3,6),(4,5)],10)
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [4,3,2,1,6,5,8,7,10,9] => [9,10,7,8,5,6,1,2,3,4] => ([(0,7),(1,6),(2,5),(3,9),(8,4),(9,8)],10)
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [6,3,2,5,4,1,8,7,10,9] => [9,10,7,8,1,4,5,2,3,6] => ([(0,6),(1,5),(2,7),(2,8),(3,9),(4,9),(7,4),(8,3)],10)
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [8,3,2,5,4,7,6,1,10,9] => [9,10,1,6,7,4,5,2,3,8] => ([(0,5),(1,6),(1,7),(1,8),(2,9),(3,9),(4,9),(6,4),(7,3),(8,2)],10)
[(1,10),(2,3),(4,5),(6,7),(8,9)] => [10,3,2,5,4,7,6,9,8,1] => [1,8,9,6,7,4,5,2,3,10] => ([(0,5),(0,6),(0,7),(0,8),(1,9),(2,9),(3,9),(4,9),(5,4),(6,3),(7,2),(8,1)],10)
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,6,5,4,3,8,7,10,9] => [9,10,7,8,3,4,5,6,1,2] => ([(0,7),(1,6),(2,5),(3,9),(8,4),(9,8)],10)
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [6,5,4,3,2,1,8,7,10,9] => [9,10,7,8,1,2,3,4,5,6] => ([(0,9),(1,5),(2,4),(6,8),(7,6),(8,3),(9,7)],10)
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [8,5,4,3,2,7,6,1,10,9] => [9,10,1,6,7,2,3,4,5,8] => ([(0,4),(1,7),(1,8),(2,9),(3,9),(5,6),(6,3),(7,5),(8,2)],10)
[(1,10),(2,5),(3,4),(6,7),(8,9)] => [10,5,4,3,2,7,6,9,8,1] => [1,8,9,6,7,2,3,4,5,10] => ([(0,6),(0,7),(0,8),(1,9),(2,9),(3,9),(4,5),(5,3),(6,4),(7,2),(8,1)],10)
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,8,5,4,7,6,3,10,9] => [9,10,3,6,7,4,5,8,1,2] => ([(0,6),(1,5),(2,7),(2,8),(3,9),(4,9),(7,4),(8,3)],10)
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [8,7,4,3,6,5,2,1,10,9] => [9,10,1,2,5,6,3,4,7,8] => ([(0,5),(1,8),(2,9),(3,9),(6,3),(7,2),(8,6),(8,7),(9,4)],10)
[(1,10),(2,7),(3,4),(5,6),(8,9)] => [10,7,4,3,6,5,2,9,8,1] => [1,8,9,2,5,6,3,4,7,10] => ([(0,6),(0,7),(1,9),(2,8),(3,8),(4,3),(5,2),(6,1),(7,4),(7,5),(8,9)],10)
[(1,2),(3,10),(4,5),(6,7),(8,9)] => [2,1,10,5,4,7,6,9,8,3] => [3,8,9,6,7,4,5,10,1,2] => ([(0,5),(1,6),(1,7),(1,8),(2,9),(3,9),(4,9),(6,4),(7,3),(8,2)],10)
[(1,10),(2,9),(3,4),(5,6),(7,8)] => [10,9,4,3,6,5,8,7,2,1] => [1,2,7,8,5,6,3,4,9,10] => ([(0,8),(1,9),(2,9),(3,9),(5,3),(6,2),(7,1),(8,5),(8,6),(8,7),(9,4)],10)
[(1,8),(2,9),(3,5),(4,6),(7,10)] => [8,9,5,6,3,4,10,1,2,7] => [7,2,1,10,4,3,6,5,9,8] => ([(0,7),(0,8),(0,9),(1,5),(1,6),(1,9),(2,5),(2,6),(2,9),(3,7),(3,8),(4,7),(4,8),(5,3),(5,4),(6,3),(6,4)],10)
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,8,7,6,5,10,9] => [9,10,5,6,7,8,3,4,1,2] => ([(0,7),(1,6),(2,5),(3,9),(8,4),(9,8)],10)
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [4,3,2,1,8,7,6,5,10,9] => [9,10,5,6,7,8,1,2,3,4] => ([(0,9),(1,8),(2,5),(6,3),(7,4),(8,6),(9,7)],10)
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [8,3,2,7,6,5,4,1,10,9] => [9,10,1,4,5,6,7,2,3,8] => ([(0,4),(1,7),(1,8),(2,9),(3,9),(5,6),(6,3),(7,5),(8,2)],10)
[(1,10),(2,3),(4,7),(5,6),(8,9)] => [10,3,2,7,6,5,4,9,8,1] => [1,8,9,4,5,6,7,2,3,10] => ([(0,6),(0,7),(0,8),(1,9),(2,9),(3,9),(4,5),(5,3),(6,4),(7,2),(8,1)],10)
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => [9,10,3,4,5,6,7,8,1,2] => ([(0,9),(1,5),(2,4),(6,8),(7,6),(8,3),(9,7)],10)
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [9,10,1,2,3,4,5,6,7,8] => ([(0,9),(1,3),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7)],10)
[(1,9),(2,7),(3,6),(4,5),(8,10)] => [9,7,6,5,4,3,2,10,1,8] => [8,1,10,2,3,4,5,6,7,9] => ([(0,8),(0,9),(1,7),(1,9),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],10)
[(1,10),(2,7),(3,6),(4,5),(8,9)] => [10,7,6,5,4,3,2,9,8,1] => [1,8,9,2,3,4,5,6,7,10] => ([(0,7),(0,8),(1,9),(2,9),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],10)
[(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,10,7,6,5,4,9,8,3] => [3,8,9,4,5,6,7,10,1,2] => ([(0,4),(1,7),(1,8),(2,9),(3,9),(5,6),(6,3),(7,5),(8,2)],10)
[(1,10),(2,9),(3,6),(4,5),(7,8)] => [10,9,6,5,4,3,8,7,2,1] => [1,2,7,8,3,4,5,6,9,10] => ([(0,8),(1,9),(2,9),(4,6),(5,4),(6,2),(7,1),(8,5),(8,7),(9,3)],10)
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,10,7,6,9,8,5] => [5,8,9,6,7,10,3,4,1,2] => ([(0,6),(1,5),(2,7),(2,8),(3,9),(4,9),(7,4),(8,3)],10)
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [4,3,2,1,10,7,6,9,8,5] => [5,8,9,6,7,10,1,2,3,4] => ([(0,8),(1,6),(1,7),(3,9),(4,9),(5,2),(6,4),(7,3),(8,5)],10)
[(1,10),(2,3),(4,9),(5,6),(7,8)] => [10,3,2,9,6,5,8,7,4,1] => [1,4,7,8,5,6,9,2,3,10] => ([(0,6),(0,7),(1,9),(2,8),(3,8),(4,3),(5,2),(6,1),(7,4),(7,5),(8,9)],10)
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,10,9,6,5,8,7,4,3] => [3,4,7,8,5,6,9,10,1,2] => ([(0,5),(1,8),(2,9),(3,9),(6,3),(7,2),(8,6),(8,7),(9,4)],10)
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [10,9,8,5,4,7,6,3,2,1] => [1,2,3,6,7,4,5,8,9,10] => ([(0,7),(2,9),(3,9),(4,3),(5,2),(6,1),(7,8),(8,4),(8,5),(9,6)],10)
[(1,10),(2,8),(3,9),(4,6),(5,7)] => [10,8,9,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,9,8,10] => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
[(1,9),(2,8),(3,7),(4,6),(5,10)] => [9,8,7,6,10,4,3,2,1,5] => [5,1,2,3,4,10,6,7,8,9] => ([(0,8),(0,9),(1,7),(3,8),(3,9),(4,3),(5,6),(6,2),(7,4),(9,5)],10)
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [5,4,3,2,1,10,9,8,7,6] => ([(0,5),(0,6),(0,7),(0,8),(0,9),(1,5),(1,6),(1,7),(1,8),(1,9),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9)],10)
[(1,7),(2,3),(4,8),(5,9),(6,10)] => [7,3,2,8,9,10,1,4,5,6] => [6,5,4,1,10,9,8,2,3,7] => ([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,4),(3,6),(3,7),(3,8),(4,5),(5,9)],10)
[(1,8),(2,5),(3,4),(6,9),(7,10)] => [8,5,4,3,2,9,10,1,6,7] => [7,6,1,10,9,2,3,4,5,8] => ([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,6),(2,8),(2,9),(3,7),(4,5),(5,3),(6,4)],10)
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,10,9,8,7] => [7,8,9,10,5,6,3,4,1,2] => ([(0,7),(1,6),(2,5),(3,9),(8,4),(9,8)],10)
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [4,3,2,1,6,5,10,9,8,7] => [7,8,9,10,5,6,1,2,3,4] => ([(0,9),(1,8),(2,5),(6,3),(7,4),(8,6),(9,7)],10)
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [6,3,2,5,4,1,10,9,8,7] => [7,8,9,10,1,4,5,2,3,6] => ([(0,8),(1,6),(1,7),(3,9),(4,9),(5,2),(6,4),(7,3),(8,5)],10)
[(1,10),(2,3),(4,5),(6,9),(7,8)] => [10,3,2,5,4,9,8,7,6,1] => [1,6,7,8,9,4,5,2,3,10] => ([(0,6),(0,7),(0,8),(1,9),(2,9),(3,9),(4,5),(5,3),(6,4),(7,2),(8,1)],10)
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,6,5,4,3,10,9,8,7] => [7,8,9,10,3,4,5,6,1,2] => ([(0,9),(1,8),(2,5),(6,3),(7,4),(8,6),(9,7)],10)
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [7,8,9,10,1,2,3,4,5,6] => ([(0,8),(1,9),(4,6),(5,4),(6,3),(7,2),(8,7),(9,5)],10)
[(1,10),(2,5),(3,4),(6,9),(7,8)] => [10,5,4,3,2,9,8,7,6,1] => [1,6,7,8,9,2,3,4,5,10] => ([(0,7),(0,8),(1,9),(2,9),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],10)
[(1,2),(3,10),(4,5),(6,9),(7,8)] => [2,1,10,5,4,9,8,7,6,3] => [3,6,7,8,9,4,5,10,1,2] => ([(0,4),(1,7),(1,8),(2,9),(3,9),(5,6),(6,3),(7,5),(8,2)],10)
[(1,10),(2,9),(3,4),(5,8),(6,7)] => [10,9,4,3,8,7,6,5,2,1] => [1,2,5,6,7,8,3,4,9,10] => ([(0,8),(1,9),(2,9),(4,6),(5,4),(6,2),(7,1),(8,5),(8,7),(9,3)],10)
[(1,7),(2,10),(3,5),(4,9),(6,8)] => [7,10,5,9,3,8,1,6,4,2] => [2,4,6,1,8,3,9,5,10,7] => ([(0,2),(0,9),(1,7),(1,9),(2,3),(2,8),(3,5),(3,7),(6,4),(7,6),(8,4),(8,5),(9,6),(9,8)],10)
[(1,9),(2,7),(3,5),(4,10),(6,8)] => [9,7,5,10,3,8,2,6,1,4] => [4,1,6,2,8,3,10,5,7,9] => ([(0,2),(0,9),(1,7),(1,9),(2,3),(2,8),(3,5),(3,7),(6,4),(7,6),(8,4),(8,5),(9,6),(9,8)],10)
[(1,5),(2,6),(3,7),(4,10),(8,9)] => [5,6,7,10,1,2,3,9,8,4] => [4,8,9,3,2,1,10,7,6,5] => ([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,4),(3,6),(3,7),(3,8),(4,5),(5,9)],10)
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,10,9,8,7,6,5] => [5,6,7,8,9,10,3,4,1,2] => ([(0,9),(1,5),(2,4),(6,8),(7,6),(8,3),(9,7)],10)
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [5,6,7,8,9,10,1,2,3,4] => ([(0,8),(1,9),(4,6),(5,4),(6,3),(7,2),(8,7),(9,5)],10)
[(1,10),(2,3),(4,9),(5,8),(6,7)] => [10,3,2,9,8,7,6,5,4,1] => [1,4,5,6,7,8,9,2,3,10] => ([(0,7),(0,8),(1,9),(2,9),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],10)
[(1,4),(2,5),(3,10),(6,9),(7,8)] => [4,5,10,1,2,9,8,7,6,3] => [3,6,7,8,9,2,1,10,5,4] => ([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,6),(2,8),(2,9),(3,7),(4,5),(5,3),(6,4)],10)
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [3,4,5,6,7,8,9,10,1,2] => ([(0,9),(1,3),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7)],10)
[(1,3),(2,10),(4,9),(5,8),(6,7)] => [3,10,1,9,8,7,6,5,4,2] => [2,4,5,6,7,8,9,1,10,3] => ([(0,8),(0,9),(1,7),(1,9),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],10)
[(1,6),(2,10),(3,9),(4,8),(5,7)] => [6,10,9,8,7,1,5,4,3,2] => [2,3,4,5,1,7,8,9,10,6] => ([(0,8),(0,9),(1,7),(3,8),(3,9),(4,3),(5,6),(6,2),(7,4),(9,5)],10)
[(1,9),(2,10),(3,8),(4,7),(5,6)] => [9,10,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,10,9] => ([(0,9),(1,9),(4,6),(5,4),(6,8),(7,5),(8,2),(8,3),(9,7)],10)
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [12,11,10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10,11,12] => ([(0,11),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,10),(9,7),(10,1),(11,9)],12)
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [2,1,10,9,8,7,6,5,4,3,12,11] => [11,12,3,4,5,6,7,8,9,10,1,2] => ([(0,11),(1,5),(2,4),(6,8),(7,6),(8,10),(9,7),(10,3),(11,9)],12)
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [12,3,2,9,8,7,6,5,4,11,10,1] => [1,10,11,4,5,6,7,8,9,2,3,12] => ([(0,8),(0,9),(0,10),(1,11),(2,11),(3,11),(4,6),(5,4),(6,7),(7,1),(8,5),(9,3),(10,2)],12)
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [2,1,12,9,8,7,6,5,4,11,10,3] => [3,10,11,4,5,6,7,8,9,12,1,2] => ([(0,4),(1,9),(1,10),(2,11),(3,11),(5,6),(6,8),(7,5),(8,3),(9,7),(10,2)],12)
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [10,3,2,9,8,7,6,5,4,1,12,11] => [11,12,1,4,5,6,7,8,9,2,3,10] => ([(0,4),(1,9),(1,10),(2,11),(3,11),(5,6),(6,8),(7,5),(8,3),(9,7),(10,2)],12)
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [12,11,4,3,8,7,6,5,10,9,2,1] => [1,2,9,10,5,6,7,8,3,4,11,12] => ([(0,10),(1,11),(2,11),(3,11),(5,7),(6,5),(7,3),(8,2),(9,1),(10,6),(10,8),(10,9),(11,4)],12)
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,8,7,6,5,10,9,12,11] => [11,12,9,10,5,6,7,8,3,4,1,2] => ([(0,9),(1,8),(2,7),(3,6),(4,11),(10,5),(11,10)],12)
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [12,3,2,11,8,7,6,5,10,9,4,1] => [1,4,9,10,5,6,7,8,11,2,3,12] => ([(0,8),(0,9),(1,11),(2,10),(3,10),(4,6),(5,4),(6,3),(7,2),(8,1),(9,5),(9,7),(10,11)],12)
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [2,1,12,11,8,7,6,5,10,9,4,3] => [3,4,9,10,5,6,7,8,11,12,1,2] => ([(0,5),(1,10),(2,11),(3,11),(6,2),(7,8),(8,9),(9,3),(10,6),(10,7),(11,4)],12)
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [4,3,2,1,8,7,6,5,10,9,12,11] => [11,12,9,10,5,6,7,8,1,2,3,4] => ([(0,11),(1,10),(2,7),(3,6),(8,4),(9,5),(10,8),(11,9)],12)
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [12,9,4,3,8,7,6,5,2,11,10,1] => [1,10,11,2,5,6,7,8,3,4,9,12] => ([(0,8),(0,9),(1,11),(2,10),(3,10),(4,6),(5,4),(6,3),(7,2),(8,1),(9,5),(9,7),(10,11)],12)
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,8,7,6,5,12,11,10,9] => [9,10,11,12,5,6,7,8,3,4,1,2] => ([(0,11),(1,10),(2,7),(3,6),(8,4),(9,5),(10,8),(11,9)],12)
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [10,9,4,3,8,7,6,5,2,1,12,11] => [11,12,1,2,5,6,7,8,3,4,9,10] => ([(0,5),(1,10),(2,11),(3,11),(6,2),(7,8),(8,9),(9,3),(10,6),(10,7),(11,4)],12)
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [4,3,2,1,8,7,6,5,12,11,10,9] => [9,10,11,12,5,6,7,8,1,2,3,4] => ([(0,11),(1,10),(2,9),(6,3),(7,4),(8,5),(9,6),(10,7),(11,8)],12)
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [12,11,10,5,4,7,6,9,8,3,2,1] => [1,2,3,8,9,6,7,4,5,10,11,12] => ([(0,9),(2,11),(3,11),(4,11),(5,4),(6,3),(7,2),(8,1),(9,10),(10,5),(10,6),(10,7),(11,8)],12)
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [2,1,10,5,4,7,6,9,8,3,12,11] => [11,12,3,8,9,6,7,4,5,10,1,2] => ([(0,7),(1,6),(2,8),(2,9),(2,10),(3,11),(4,11),(5,11),(8,5),(9,4),(10,3)],12)
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [12,3,2,5,4,7,6,9,8,11,10,1] => [1,10,11,8,9,6,7,4,5,2,3,12] => ([(0,6),(0,7),(0,8),(0,9),(0,10),(1,11),(2,11),(3,11),(4,11),(5,11),(6,5),(7,4),(8,3),(9,2),(10,1)],12)
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [2,1,12,5,4,7,6,9,8,11,10,3] => [3,10,11,8,9,6,7,4,5,12,1,2] => ([(0,6),(1,7),(1,8),(1,9),(1,10),(2,11),(3,11),(4,11),(5,11),(7,5),(8,4),(9,3),(10,2)],12)
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [10,3,2,5,4,7,6,9,8,1,12,11] => [11,12,1,8,9,6,7,4,5,2,3,10] => ([(0,6),(1,7),(1,8),(1,9),(1,10),(2,11),(3,11),(4,11),(5,11),(7,5),(8,4),(9,3),(10,2)],12)
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [12,11,4,3,10,7,6,9,8,5,2,1] => [1,2,5,8,9,6,7,10,3,4,11,12] => ([(0,9),(2,11),(3,10),(4,10),(5,2),(6,4),(7,3),(8,6),(8,7),(9,5),(9,8),(10,11),(11,1)],12)
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [2,1,4,3,10,7,6,9,8,5,12,11] => [11,12,5,8,9,6,7,10,3,4,1,2] => ([(0,8),(1,7),(2,6),(3,9),(3,10),(4,11),(5,11),(9,5),(10,4)],12)
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [12,3,2,11,10,7,6,9,8,5,4,1] => [1,4,5,8,9,6,7,10,11,2,3,12] => ([(0,7),(0,8),(1,11),(2,11),(3,10),(4,10),(5,2),(6,1),(7,3),(8,9),(9,5),(9,6),(11,4)],12)
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [2,1,12,11,10,7,6,9,8,5,4,3] => [3,4,5,8,9,6,7,10,11,12,1,2] => ([(0,9),(1,5),(3,11),(4,11),(6,4),(7,3),(8,2),(9,10),(10,6),(10,7),(11,8)],12)
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [4,3,2,1,10,7,6,9,8,5,12,11] => [11,12,5,8,9,6,7,10,1,2,3,4] => ([(0,10),(1,6),(2,8),(2,9),(4,11),(5,11),(7,3),(8,5),(9,4),(10,7)],12)
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [12,5,4,3,2,7,6,9,8,11,10,1] => [1,10,11,8,9,6,7,2,3,4,5,12] => ([(0,7),(0,8),(0,9),(0,10),(1,11),(2,11),(3,11),(4,11),(5,6),(6,4),(7,5),(8,3),(9,2),(10,1)],12)
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [2,1,4,3,12,7,6,9,8,11,10,5] => [5,10,11,8,9,6,7,12,3,4,1,2] => ([(0,7),(1,6),(2,8),(2,9),(2,10),(3,11),(4,11),(5,11),(8,5),(9,4),(10,3)],12)
[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [10,5,4,3,2,7,6,9,8,1,12,11] => [11,12,1,8,9,6,7,2,3,4,5,10] => ([(0,5),(1,8),(1,9),(1,10),(2,11),(3,11),(4,11),(6,7),(7,4),(8,6),(9,3),(10,2)],12)
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [4,3,2,1,12,7,6,9,8,11,10,5] => [5,10,11,8,9,6,7,12,1,2,3,4] => ([(0,10),(1,7),(1,8),(1,9),(3,11),(4,11),(5,11),(6,2),(7,5),(8,4),(9,3),(10,6)],12)
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [12,11,8,5,4,7,6,3,10,9,2,1] => [1,2,9,10,3,6,7,4,5,8,11,12] => ([(0,9),(2,11),(3,10),(4,10),(5,2),(6,4),(7,3),(8,6),(8,7),(9,5),(9,8),(10,11),(11,1)],12)
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [2,1,8,5,4,7,6,3,10,9,12,11] => [11,12,9,10,3,6,7,4,5,8,1,2] => ([(0,8),(1,7),(2,6),(3,9),(3,10),(4,11),(5,11),(9,5),(10,4)],12)
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [12,3,2,5,4,7,6,11,10,9,8,1] => [1,8,9,10,11,6,7,4,5,2,3,12] => ([(0,7),(0,8),(0,9),(0,10),(1,11),(2,11),(3,11),(4,11),(5,6),(6,4),(7,5),(8,3),(9,2),(10,1)],12)
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [2,1,12,5,4,7,6,11,10,9,8,3] => [3,8,9,10,11,6,7,4,5,12,1,2] => ([(0,5),(1,8),(1,9),(1,10),(2,11),(3,11),(4,11),(6,7),(7,4),(8,6),(9,3),(10,2)],12)
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [8,3,2,5,4,7,6,1,10,9,12,11] => [11,12,9,10,1,6,7,4,5,2,3,8] => ([(0,7),(1,6),(2,8),(2,9),(2,10),(3,11),(4,11),(5,11),(8,5),(9,4),(10,3)],12)
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [12,9,8,5,4,7,6,3,2,11,10,1] => [1,10,11,2,3,6,7,4,5,8,9,12] => ([(0,7),(0,8),(1,11),(2,11),(3,10),(4,10),(5,2),(6,1),(7,3),(8,9),(9,5),(9,6),(11,4)],12)
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [2,1,8,5,4,7,6,3,12,11,10,9] => [9,10,11,12,3,6,7,4,5,8,1,2] => ([(0,10),(1,6),(2,8),(2,9),(4,11),(5,11),(7,3),(8,5),(9,4),(10,7)],12)
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [10,9,8,5,4,7,6,3,2,1,12,11] => [11,12,1,2,3,6,7,4,5,8,9,10] => ([(0,9),(1,5),(3,11),(4,11),(6,4),(7,3),(8,2),(9,10),(10,6),(10,7),(11,8)],12)
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [8,3,2,5,4,7,6,1,12,11,10,9] => [9,10,11,12,1,6,7,4,5,2,3,8] => ([(0,10),(1,7),(1,8),(1,9),(3,11),(4,11),(5,11),(6,2),(7,5),(8,4),(9,3),(10,6)],12)
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [12,5,4,3,2,7,6,11,10,9,8,1] => [1,8,9,10,11,6,7,2,3,4,5,12] => ([(0,8),(0,9),(0,10),(1,11),(2,11),(3,11),(4,6),(5,7),(6,3),(7,2),(8,4),(9,5),(10,1)],12)
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [2,1,4,3,12,7,6,11,10,9,8,5] => [5,8,9,10,11,6,7,12,3,4,1,2] => ([(0,6),(1,5),(2,9),(2,10),(3,11),(4,11),(7,8),(8,4),(9,3),(10,7)],12)
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [8,5,4,3,2,7,6,1,10,9,12,11] => [11,12,9,10,1,6,7,2,3,4,5,8] => ([(0,6),(1,5),(2,9),(2,10),(3,11),(4,11),(7,8),(8,4),(9,3),(10,7)],12)
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [4,3,2,1,12,7,6,11,10,9,8,5] => [5,8,9,10,11,6,7,12,1,2,3,4] => ([(0,10),(1,8),(1,9),(3,11),(4,11),(5,7),(6,2),(7,4),(8,5),(9,3),(10,6)],12)
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [8,5,4,3,2,7,6,1,12,11,10,9] => [9,10,11,12,1,6,7,2,3,4,5,8] => ([(0,10),(1,8),(1,9),(3,11),(4,11),(5,7),(6,2),(7,4),(8,5),(9,3),(10,6)],12)
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [12,11,10,9,6,5,8,7,4,3,2,1] => [1,2,3,4,7,8,5,6,9,10,11,12] => ([(0,9),(2,11),(3,11),(4,1),(5,10),(6,3),(7,2),(8,4),(9,5),(10,6),(10,7),(11,8)],12)
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,10,9,6,5,8,7,4,3,12,11] => [11,12,3,4,7,8,5,6,9,10,1,2] => ([(0,7),(1,6),(2,10),(3,11),(4,11),(8,4),(9,3),(10,8),(10,9),(11,5)],12)
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [12,3,2,9,6,5,8,7,4,11,10,1] => [1,10,11,4,7,8,5,6,9,2,3,12] => ([(0,7),(0,8),(0,9),(1,11),(2,11),(3,10),(4,10),(5,4),(6,3),(7,2),(8,1),(9,5),(9,6),(10,11)],12)
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [2,1,12,9,6,5,8,7,4,11,10,3] => [3,10,11,4,7,8,5,6,9,12,1,2] => ([(0,5),(1,8),(1,9),(2,11),(3,10),(4,10),(6,4),(7,3),(8,2),(9,6),(9,7),(10,11)],12)
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [10,3,2,9,6,5,8,7,4,1,12,11] => [11,12,1,4,7,8,5,6,9,2,3,10] => ([(0,5),(1,8),(1,9),(2,11),(3,10),(4,10),(6,4),(7,3),(8,2),(9,6),(9,7),(10,11)],12)
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [12,11,4,3,6,5,8,7,10,9,2,1] => [1,2,9,10,7,8,5,6,3,4,11,12] => ([(0,10),(1,11),(2,11),(3,11),(4,11),(6,4),(7,3),(8,2),(9,1),(10,6),(10,7),(10,8),(10,9),(11,5)],12)
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [2,1,4,3,6,5,8,7,10,9,12,11] => [11,12,9,10,7,8,5,6,3,4,1,2] => ([(0,11),(1,10),(2,9),(3,8),(4,7),(5,6)],12)
[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => [12,3,2,11,6,5,8,7,10,9,4,1] => [1,4,9,10,7,8,5,6,11,2,3,12] => ([(0,8),(0,9),(1,11),(2,11),(3,11),(4,10),(5,3),(6,2),(7,1),(8,4),(9,5),(9,6),(9,7),(11,10)],12)
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [2,1,12,11,6,5,8,7,10,9,4,3] => [3,4,9,10,7,8,5,6,11,12,1,2] => ([(0,6),(1,10),(2,11),(3,11),(4,11),(7,4),(8,3),(9,2),(10,7),(10,8),(10,9),(11,5)],12)
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [4,3,2,1,6,5,8,7,10,9,12,11] => [11,12,9,10,7,8,5,6,1,2,3,4] => ([(0,9),(1,8),(2,7),(3,6),(4,11),(10,5),(11,10)],12)
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [12,9,4,3,6,5,8,7,2,11,10,1] => [1,10,11,2,7,8,5,6,3,4,9,12] => ([(0,8),(0,9),(1,11),(2,11),(3,11),(4,10),(5,3),(6,2),(7,1),(8,4),(9,5),(9,6),(9,7),(11,10)],12)
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [2,1,4,3,6,5,8,7,12,11,10,9] => [9,10,11,12,7,8,5,6,3,4,1,2] => ([(0,9),(1,8),(2,7),(3,6),(4,11),(10,5),(11,10)],12)
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [10,9,4,3,6,5,8,7,2,1,12,11] => [11,12,1,2,7,8,5,6,3,4,9,10] => ([(0,6),(1,10),(2,11),(3,11),(4,11),(7,4),(8,3),(9,2),(10,7),(10,8),(10,9),(11,5)],12)
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [4,3,2,1,6,5,8,7,12,11,10,9] => [9,10,11,12,7,8,5,6,1,2,3,4] => ([(0,11),(1,10),(2,7),(3,6),(8,4),(9,5),(10,8),(11,9)],12)
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [12,11,10,5,4,9,8,7,6,3,2,1] => [1,2,3,6,7,8,9,4,5,10,11,12] => ([(0,9),(2,11),(3,11),(4,6),(5,4),(6,3),(7,2),(8,1),(9,10),(10,5),(10,7),(11,8)],12)
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [2,1,10,5,4,9,8,7,6,3,12,11] => [11,12,3,6,7,8,9,4,5,10,1,2] => ([(0,6),(1,5),(2,9),(2,10),(3,11),(4,11),(7,8),(8,4),(9,3),(10,7)],12)
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [12,3,2,5,4,9,8,7,6,11,10,1] => [1,10,11,6,7,8,9,4,5,2,3,12] => ([(0,7),(0,8),(0,9),(0,10),(1,11),(2,11),(3,11),(4,11),(5,6),(6,4),(7,5),(8,3),(9,2),(10,1)],12)
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [2,1,12,5,4,9,8,7,6,11,10,3] => [3,10,11,6,7,8,9,4,5,12,1,2] => ([(0,5),(1,8),(1,9),(1,10),(2,11),(3,11),(4,11),(6,7),(7,4),(8,6),(9,3),(10,2)],12)
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [10,3,2,5,4,9,8,7,6,1,12,11] => [11,12,1,6,7,8,9,4,5,2,3,10] => ([(0,5),(1,8),(1,9),(1,10),(2,11),(3,11),(4,11),(6,7),(7,4),(8,6),(9,3),(10,2)],12)
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [12,11,4,3,10,9,8,7,6,5,2,1] => [1,2,5,6,7,8,9,10,3,4,11,12] => ([(0,10),(1,11),(2,11),(4,6),(5,4),(6,8),(7,5),(8,2),(9,1),(10,7),(10,9),(11,3)],12)
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,10,9,8,7,6,5,12,11] => [11,12,5,6,7,8,9,10,3,4,1,2] => ([(0,7),(1,6),(2,5),(3,11),(8,10),(9,4),(10,9),(11,8)],12)
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [12,3,2,11,10,9,8,7,6,5,4,1] => [1,4,5,6,7,8,9,10,11,2,3,12] => ([(0,9),(0,10),(1,11),(2,11),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7),(10,1)],12)
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,12,11,10,9,8,7,6,5,4,3] => [3,4,5,6,7,8,9,10,11,12,1,2] => ([(0,11),(1,3),(4,6),(5,4),(6,8),(7,5),(8,10),(9,7),(10,2),(11,9)],12)
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [4,3,2,1,10,9,8,7,6,5,12,11] => [11,12,5,6,7,8,9,10,1,2,3,4] => ([(0,10),(1,11),(2,5),(6,8),(7,6),(8,4),(9,3),(10,9),(11,7)],12)
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [12,5,4,3,2,9,8,7,6,11,10,1] => [1,10,11,6,7,8,9,2,3,4,5,12] => ([(0,8),(0,9),(0,10),(1,11),(2,11),(3,11),(4,6),(5,7),(6,3),(7,2),(8,4),(9,5),(10,1)],12)
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,12,9,8,7,6,11,10,5] => [5,10,11,6,7,8,9,12,3,4,1,2] => ([(0,6),(1,5),(2,9),(2,10),(3,11),(4,11),(7,8),(8,4),(9,3),(10,7)],12)
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [10,5,4,3,2,9,8,7,6,1,12,11] => [11,12,1,6,7,8,9,2,3,4,5,10] => ([(0,4),(1,9),(1,10),(2,11),(3,11),(5,7),(6,8),(7,3),(8,2),(9,5),(10,6)],12)
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [4,3,2,1,12,9,8,7,6,11,10,5] => [5,10,11,6,7,8,9,12,1,2,3,4] => ([(0,10),(1,8),(1,9),(3,11),(4,11),(5,7),(6,2),(7,4),(8,5),(9,3),(10,6)],12)
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [12,11,6,5,4,3,8,7,10,9,2,1] => [1,2,9,10,7,8,3,4,5,6,11,12] => ([(0,10),(1,11),(2,11),(3,11),(5,7),(6,5),(7,3),(8,2),(9,1),(10,6),(10,8),(10,9),(11,4)],12)
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,6,5,4,3,8,7,10,9,12,11] => [11,12,9,10,7,8,3,4,5,6,1,2] => ([(0,9),(1,8),(2,7),(3,6),(4,11),(10,5),(11,10)],12)
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [12,3,2,5,4,11,8,7,10,9,6,1] => [1,6,9,10,7,8,11,4,5,2,3,12] => ([(0,7),(0,8),(0,9),(1,11),(2,11),(3,10),(4,10),(5,4),(6,3),(7,2),(8,1),(9,5),(9,6),(10,11)],12)
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [2,1,12,5,4,11,8,7,10,9,6,3] => [3,6,9,10,7,8,11,4,5,12,1,2] => ([(0,5),(1,8),(1,9),(2,11),(3,10),(4,10),(6,4),(7,3),(8,2),(9,6),(9,7),(10,11)],12)
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [6,3,2,5,4,1,8,7,10,9,12,11] => [11,12,9,10,7,8,1,4,5,2,3,6] => ([(0,8),(1,7),(2,6),(3,9),(3,10),(4,11),(5,11),(9,5),(10,4)],12)
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [12,9,6,5,4,3,8,7,2,11,10,1] => [1,10,11,2,7,8,3,4,5,6,9,12] => ([(0,8),(0,9),(1,11),(2,10),(3,10),(4,6),(5,4),(6,3),(7,2),(8,1),(9,5),(9,7),(10,11)],12)
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,6,5,4,3,8,7,12,11,10,9] => [9,10,11,12,7,8,3,4,5,6,1,2] => ([(0,11),(1,10),(2,7),(3,6),(8,4),(9,5),(10,8),(11,9)],12)
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [10,9,6,5,4,3,8,7,2,1,12,11] => [11,12,1,2,7,8,3,4,5,6,9,10] => ([(0,5),(1,10),(2,11),(3,11),(6,2),(7,8),(8,9),(9,3),(10,6),(10,7),(11,4)],12)
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [6,3,2,5,4,1,8,7,12,11,10,9] => [9,10,11,12,7,8,1,4,5,2,3,6] => ([(0,10),(1,6),(2,8),(2,9),(4,11),(5,11),(7,3),(8,5),(9,4),(10,7)],12)
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [12,5,4,3,2,11,8,7,10,9,6,1] => [1,6,9,10,7,8,11,2,3,4,5,12] => ([(0,8),(0,9),(1,11),(2,10),(3,10),(4,1),(5,4),(6,3),(7,2),(8,5),(9,6),(9,7),(10,11)],12)
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,12,11,8,7,10,9,6,5] => [5,6,9,10,7,8,11,12,3,4,1,2] => ([(0,7),(1,6),(2,10),(3,11),(4,11),(8,4),(9,3),(10,8),(10,9),(11,5)],12)
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [6,5,4,3,2,1,8,7,10,9,12,11] => [11,12,9,10,7,8,1,2,3,4,5,6] => ([(0,7),(1,6),(2,5),(3,11),(8,10),(9,4),(10,9),(11,8)],12)
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [4,3,2,1,12,11,8,7,10,9,6,5] => [5,6,9,10,7,8,11,12,1,2,3,4] => ([(0,9),(1,10),(3,11),(4,11),(6,2),(7,4),(8,3),(9,6),(10,7),(10,8),(11,5)],12)
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [6,5,4,3,2,1,8,7,12,11,10,9] => [9,10,11,12,7,8,1,2,3,4,5,6] => ([(0,10),(1,11),(2,5),(6,8),(7,6),(8,4),(9,3),(10,9),(11,7)],12)
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [12,11,10,7,6,5,4,9,8,3,2,1] => [1,2,3,8,9,4,5,6,7,10,11,12] => ([(0,9),(2,11),(3,11),(4,6),(5,4),(6,3),(7,2),(8,1),(9,10),(10,5),(10,7),(11,8)],12)
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [2,1,10,7,6,5,4,9,8,3,12,11] => [11,12,3,8,9,4,5,6,7,10,1,2] => ([(0,6),(1,5),(2,9),(2,10),(3,11),(4,11),(7,8),(8,4),(9,3),(10,7)],12)
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [12,3,2,7,6,5,4,9,8,11,10,1] => [1,10,11,8,9,4,5,6,7,2,3,12] => ([(0,7),(0,8),(0,9),(0,10),(1,11),(2,11),(3,11),(4,11),(5,6),(6,4),(7,5),(8,3),(9,2),(10,1)],12)
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [2,1,12,7,6,5,4,9,8,11,10,3] => [3,10,11,8,9,4,5,6,7,12,1,2] => ([(0,5),(1,8),(1,9),(1,10),(2,11),(3,11),(4,11),(6,7),(7,4),(8,6),(9,3),(10,2)],12)
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [10,3,2,7,6,5,4,9,8,1,12,11] => [11,12,1,8,9,4,5,6,7,2,3,10] => ([(0,5),(1,8),(1,9),(1,10),(2,11),(3,11),(4,11),(6,7),(7,4),(8,6),(9,3),(10,2)],12)
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [12,11,4,3,6,5,10,9,8,7,2,1] => [1,2,7,8,9,10,5,6,3,4,11,12] => ([(0,10),(1,11),(2,11),(3,11),(5,7),(6,5),(7,3),(8,2),(9,1),(10,6),(10,8),(10,9),(11,4)],12)
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,10,9,8,7,12,11] => [11,12,7,8,9,10,5,6,3,4,1,2] => ([(0,9),(1,8),(2,7),(3,6),(4,11),(10,5),(11,10)],12)
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [12,3,2,11,6,5,10,9,8,7,4,1] => [1,4,7,8,9,10,5,6,11,2,3,12] => ([(0,8),(0,9),(1,11),(2,10),(3,10),(4,6),(5,4),(6,3),(7,2),(8,1),(9,5),(9,7),(10,11)],12)
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,12,11,6,5,10,9,8,7,4,3] => [3,4,7,8,9,10,5,6,11,12,1,2] => ([(0,5),(1,10),(2,11),(3,11),(6,2),(7,8),(8,9),(9,3),(10,6),(10,7),(11,4)],12)
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [4,3,2,1,6,5,10,9,8,7,12,11] => [11,12,7,8,9,10,5,6,1,2,3,4] => ([(0,11),(1,10),(2,7),(3,6),(8,4),(9,5),(10,8),(11,9)],12)
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [12,7,4,3,6,5,2,9,8,11,10,1] => [1,10,11,8,9,2,5,6,3,4,7,12] => ([(0,7),(0,8),(0,9),(1,11),(2,11),(3,10),(4,10),(5,4),(6,3),(7,2),(8,1),(9,5),(9,6),(10,11)],12)
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,12,9,8,11,10,7] => [7,10,11,8,9,12,5,6,3,4,1,2] => ([(0,8),(1,7),(2,6),(3,9),(3,10),(4,11),(5,11),(9,5),(10,4)],12)
[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [10,7,4,3,6,5,2,9,8,1,12,11] => [11,12,1,8,9,2,5,6,3,4,7,10] => ([(0,5),(1,8),(1,9),(2,11),(3,10),(4,10),(6,4),(7,3),(8,2),(9,6),(9,7),(10,11)],12)
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [4,3,2,1,6,5,12,9,8,11,10,7] => [7,10,11,8,9,12,5,6,1,2,3,4] => ([(0,10),(1,6),(2,8),(2,9),(4,11),(5,11),(7,3),(8,5),(9,4),(10,7)],12)
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [12,11,8,7,6,5,4,3,10,9,2,1] => [1,2,9,10,3,4,5,6,7,8,11,12] => ([(0,10),(1,11),(2,11),(4,6),(5,4),(6,8),(7,5),(8,2),(9,1),(10,7),(10,9),(11,3)],12)
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,8,7,6,5,4,3,10,9,12,11] => [11,12,9,10,3,4,5,6,7,8,1,2] => ([(0,7),(1,6),(2,5),(3,11),(8,10),(9,4),(10,9),(11,8)],12)
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [12,3,2,7,6,5,4,11,10,9,8,1] => [1,8,9,10,11,4,5,6,7,2,3,12] => ([(0,8),(0,9),(0,10),(1,11),(2,11),(3,11),(4,6),(5,7),(6,3),(7,2),(8,4),(9,5),(10,1)],12)
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [2,1,12,7,6,5,4,11,10,9,8,3] => [3,8,9,10,11,4,5,6,7,12,1,2] => ([(0,4),(1,9),(1,10),(2,11),(3,11),(5,7),(6,8),(7,3),(8,2),(9,5),(10,6)],12)
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [8,3,2,7,6,5,4,1,10,9,12,11] => [11,12,9,10,1,4,5,6,7,2,3,8] => ([(0,6),(1,5),(2,9),(2,10),(3,11),(4,11),(7,8),(8,4),(9,3),(10,7)],12)
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [12,9,8,7,6,5,4,3,2,11,10,1] => [1,10,11,2,3,4,5,6,7,8,9,12] => ([(0,9),(0,10),(1,11),(2,11),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7),(10,1)],12)
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,8,7,6,5,4,3,12,11,10,9] => [9,10,11,12,3,4,5,6,7,8,1,2] => ([(0,10),(1,11),(2,5),(6,8),(7,6),(8,4),(9,3),(10,9),(11,7)],12)
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [10,9,8,7,6,5,4,3,2,1,12,11] => [11,12,1,2,3,4,5,6,7,8,9,10] => ([(0,11),(1,3),(4,6),(5,4),(6,8),(7,5),(8,10),(9,7),(10,2),(11,9)],12)
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [8,3,2,7,6,5,4,1,12,11,10,9] => [9,10,11,12,1,4,5,6,7,2,3,8] => ([(0,10),(1,8),(1,9),(3,11),(4,11),(5,7),(6,2),(7,4),(8,5),(9,3),(10,6)],12)
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [12,7,4,3,6,5,2,11,10,9,8,1] => [1,8,9,10,11,2,5,6,3,4,7,12] => ([(0,8),(0,9),(1,11),(2,10),(3,10),(4,1),(5,4),(6,3),(7,2),(8,5),(9,6),(9,7),(10,11)],12)
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [2,1,4,3,6,5,12,11,10,9,8,7] => [7,8,9,10,11,12,5,6,3,4,1,2] => ([(0,7),(1,6),(2,5),(3,11),(8,10),(9,4),(10,9),(11,8)],12)
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [8,7,4,3,6,5,2,1,10,9,12,11] => [11,12,9,10,1,2,5,6,3,4,7,8] => ([(0,7),(1,6),(2,10),(3,11),(4,11),(8,4),(9,3),(10,8),(10,9),(11,5)],12)
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [4,3,2,1,6,5,12,11,10,9,8,7] => [7,8,9,10,11,12,5,6,1,2,3,4] => ([(0,10),(1,11),(2,5),(6,8),(7,6),(8,4),(9,3),(10,9),(11,7)],12)
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [8,7,4,3,6,5,2,1,12,11,10,9] => [9,10,11,12,1,2,5,6,3,4,7,8] => ([(0,9),(1,10),(3,11),(4,11),(6,2),(7,4),(8,3),(9,6),(10,7),(10,8),(11,5)],12)
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [12,11,6,5,4,3,10,9,8,7,2,1] => [1,2,7,8,9,10,3,4,5,6,11,12] => ([(0,10),(1,11),(2,11),(4,8),(5,9),(6,4),(7,5),(8,2),(9,1),(10,6),(10,7),(11,3)],12)
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,6,5,4,3,10,9,8,7,12,11] => [11,12,7,8,9,10,3,4,5,6,1,2] => ([(0,11),(1,10),(2,7),(3,6),(8,4),(9,5),(10,8),(11,9)],12)
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [12,3,2,5,4,11,10,9,8,7,6,1] => [1,6,7,8,9,10,11,4,5,2,3,12] => ([(0,8),(0,9),(0,10),(1,11),(2,11),(3,11),(4,6),(5,4),(6,7),(7,1),(8,5),(9,3),(10,2)],12)
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [2,1,12,5,4,11,10,9,8,7,6,3] => [3,6,7,8,9,10,11,4,5,12,1,2] => ([(0,4),(1,9),(1,10),(2,11),(3,11),(5,6),(6,8),(7,5),(8,3),(9,7),(10,2)],12)
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [6,3,2,5,4,1,10,9,8,7,12,11] => [11,12,7,8,9,10,1,4,5,2,3,6] => ([(0,10),(1,6),(2,8),(2,9),(4,11),(5,11),(7,3),(8,5),(9,4),(10,7)],12)
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [12,7,6,5,4,3,2,9,8,11,10,1] => [1,10,11,8,9,2,3,4,5,6,7,12] => ([(0,8),(0,9),(0,10),(1,11),(2,11),(3,11),(4,6),(5,4),(6,7),(7,1),(8,5),(9,3),(10,2)],12)
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [2,1,6,5,4,3,12,9,8,11,10,7] => [7,10,11,8,9,12,3,4,5,6,1,2] => ([(0,10),(1,6),(2,8),(2,9),(4,11),(5,11),(7,3),(8,5),(9,4),(10,7)],12)
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [10,7,6,5,4,3,2,9,8,1,12,11] => [11,12,1,8,9,2,3,4,5,6,7,10] => ([(0,4),(1,9),(1,10),(2,11),(3,11),(5,6),(6,8),(7,5),(8,3),(9,7),(10,2)],12)
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [6,3,2,5,4,1,12,9,8,11,10,7] => [7,10,11,8,9,12,1,4,5,2,3,6] => ([(0,8),(0,9),(1,6),(1,7),(2,10),(3,10),(4,11),(5,11),(6,3),(7,2),(8,5),(9,4)],12)
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [12,5,4,3,2,11,10,9,8,7,6,1] => [1,6,7,8,9,10,11,2,3,4,5,12] => ([(0,9),(0,10),(1,11),(2,11),(3,4),(4,8),(5,3),(6,7),(7,1),(8,2),(9,6),(10,5)],12)
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,12,11,10,9,8,7,6,5] => [5,6,7,8,9,10,11,12,3,4,1,2] => ([(0,11),(1,5),(2,4),(6,8),(7,6),(8,10),(9,7),(10,3),(11,9)],12)
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [6,5,4,3,2,1,10,9,8,7,12,11] => [11,12,7,8,9,10,1,2,3,4,5,6] => ([(0,10),(1,11),(2,5),(6,8),(7,6),(8,4),(9,3),(10,9),(11,7)],12)
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [4,3,2,1,12,11,10,9,8,7,6,5] => [5,6,7,8,9,10,11,12,1,2,3,4] => ([(0,10),(1,11),(4,6),(5,4),(6,8),(7,5),(8,3),(9,2),(10,9),(11,7)],12)
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [6,5,4,3,2,1,12,9,8,11,10,7] => [7,10,11,8,9,12,1,2,3,4,5,6] => ([(0,10),(1,8),(1,9),(3,11),(4,11),(5,6),(6,2),(7,5),(8,4),(9,3),(10,7)],12)
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [12,7,6,5,4,3,2,11,10,9,8,1] => [1,8,9,10,11,2,3,4,5,6,7,12] => ([(0,9),(0,10),(1,11),(2,11),(3,4),(4,8),(5,3),(6,7),(7,1),(8,2),(9,6),(10,5)],12)
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,6,5,4,3,12,11,10,9,8,7] => [7,8,9,10,11,12,3,4,5,6,1,2] => ([(0,10),(1,11),(2,5),(6,8),(7,6),(8,4),(9,3),(10,9),(11,7)],12)
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [8,7,6,5,4,3,2,1,10,9,12,11] => [11,12,9,10,1,2,3,4,5,6,7,8] => ([(0,11),(1,5),(2,4),(6,8),(7,6),(8,10),(9,7),(10,3),(11,9)],12)
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [6,3,2,5,4,1,12,11,10,9,8,7] => [7,8,9,10,11,12,1,4,5,2,3,6] => ([(0,10),(1,8),(1,9),(3,11),(4,11),(5,6),(6,2),(7,5),(8,4),(9,3),(10,7)],12)
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [8,7,6,5,4,3,2,1,12,11,10,9] => [9,10,11,12,1,2,3,4,5,6,7,8] => ([(0,10),(1,11),(4,6),(5,4),(6,8),(7,5),(8,3),(9,2),(10,9),(11,7)],12)
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [6,5,4,3,2,1,12,11,10,9,8,7] => [7,8,9,10,11,12,1,2,3,4,5,6] => ([(0,11),(1,10),(4,8),(5,9),(6,4),(7,5),(8,2),(9,3),(10,6),(11,7)],12)
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [6,5,4,3,2,1,12,11,10,9,8,7] => ([(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11)],12)
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$