Identifier
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
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
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.
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.