Identifier
-
Mp00058:
Perfect matchings
—to permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
St000883: Permutations ⟶ ℤ
Values
[(1,2)] => [2,1] => [2,1] => [1] => 1
[(1,2),(3,4)] => [2,1,4,3] => [2,1,4,3] => [2,1,3] => 2
[(1,3),(2,4)] => [3,4,1,2] => [2,4,3,1] => [2,3,1] => 1
[(1,4),(2,3)] => [4,3,2,1] => [4,1,2,3] => [1,2,3] => 1
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,5] => 4
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [2,4,3,1,6,5] => [2,4,3,1,5] => 2
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [4,1,2,3,6,5] => [4,1,2,3,5] => 1
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [4,5,2,6,3,1] => [4,5,2,3,1] => 2
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [6,5,2,1,4,3] => [5,2,1,4,3] => 4
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [6,3,1,5,2,4] => [3,1,5,2,4] => 1
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [3,1,6,5,4,2] => [3,1,5,4,2] => 5
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [2,3,6,4,5,1] => [2,3,4,5,1] => 1
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [5,4,3,6,1,2] => [5,4,3,1,2] => 1
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,1,4,6,5,3] => [2,1,4,5,3] => 2
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [2,1,6,3,4,5] => [2,1,3,4,5] => 2
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [5,6,3,2,4,1] => [5,3,2,4,1] => 2
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [3,6,2,4,1,5] => [3,2,4,1,5] => 2
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [2,6,1,3,5,4] => [2,1,3,5,4] => 4
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [6,1,2,3,4,5] => [1,2,3,4,5] => 1
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [2,1,6,3,4,5,8,7] => [2,1,6,3,4,5,7] => 2
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [6,1,2,3,4,5,8,7] => [6,1,2,3,4,5,7] => 1
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [8,1,4,2,6,3,5,7] => [1,4,2,6,3,5,7] => 1
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [2,3,4,8,5,6,7,1] => [2,3,4,5,6,7,1] => 1
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [8,7,5,6,1,2,3,4] => [7,5,6,1,2,3,4] => 1
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [4,1,2,3,8,5,6,7] => [4,1,2,3,5,6,7] => 1
[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [2,1,8,3,4,5,6,7] => [2,1,3,4,5,6,7] => 2
[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 1
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 1
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Description
The number of longest increasing subsequences of a permutation.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.
This map is undefined for the empty permutation.
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
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