Identifier
Mp00058:
Perfect matchings
—to permutation⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
[(1,2)] => [2,1] => [[.,.],.]
[(1,2),(3,4)] => [2,1,4,3] => [[.,.],[[.,.],.]]
[(1,3),(2,4)] => [3,4,1,2] => [[.,[.,.]],[.,.]]
[(1,4),(2,3)] => [4,3,2,1] => [[[[.,.],.],.],.]
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]]
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]]
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [[[[.,.],.],[.,.]],[.,.]]
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.]
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [[[[.,.],[.,.]],.],[.,.]]
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]]
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]]
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]]
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]]
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [[.,[.,.]],[[[.,.],.],.]]
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [[.,[[.,.],.]],[[.,.],.]]
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]]
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [[.,.],[[[[.,.],.],[[.,.],.]],.]]
[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]]
[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => [[[[.,.],.],[[[.,.],.],.]],[.,.]]
[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.]
[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.]
[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]]
[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
>>> Load all 154 entries. <<<Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
searching the database
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