Identifier
Values
[1,0] => [(1,2)] => [2,1] => [[1],[2]] => 2
[1,0,1,0] => [(1,2),(3,4)] => [2,1,4,3] => [[1,3],[2,4]] => 2
[1,1,0,0] => [(1,4),(2,3)] => [3,4,2,1] => [[1,4],[2],[3]] => 3
[1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => 2
[1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => [[1,3,6],[2,4],[5]] => 5
[1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => [[1,4,5],[2,6],[3]] => 3
[1,1,0,1,0,0] => [(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => [[1,4,6],[2,5],[3]] => 3
[1,1,1,0,0,0] => [(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => [[1,5,6],[2],[3],[4]] => 4
[1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => 2
[1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,7,8,6,5] => [[1,3,5,8],[2,4,6],[7]] => 7
[1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => [2,1,5,6,4,3,8,7] => [[1,3,6,7],[2,4,8],[5]] => 5
[1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => [2,1,5,7,4,8,6,3] => [[1,3,6,8],[2,4,7],[5]] => 5
[1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => [2,1,6,7,8,5,4,3] => [[1,3,7,8],[2,4],[5],[6]] => 6
[1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => [3,4,2,1,6,5,8,7] => [[1,4,5,7],[2,6,8],[3]] => 3
[1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => [3,4,2,1,7,8,6,5] => [[1,4,5,8],[2,6],[3,7]] => 3
[1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => [3,5,2,6,4,1,8,7] => [[1,4,6,7],[2,5,8],[3]] => 3
[1,1,0,1,0,1,0,0] => [(1,8),(2,3),(4,5),(6,7)] => [3,5,2,7,4,8,6,1] => [[1,4,6,8],[2,5,7],[3]] => 3
[1,1,0,1,1,0,0,0] => [(1,8),(2,3),(4,7),(5,6)] => [3,6,2,7,8,5,4,1] => [[1,4,7,8],[2,5],[3],[6]] => 6
[1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => [4,5,6,3,2,1,8,7] => [[1,5,6,7],[2,8],[3],[4]] => 4
[1,1,1,0,0,1,0,0] => [(1,8),(2,5),(3,4),(6,7)] => [4,5,7,3,2,8,6,1] => [[1,5,6,8],[2,7],[3],[4]] => 4
[1,1,1,0,1,0,0,0] => [(1,8),(2,7),(3,4),(5,6)] => [4,6,7,3,8,5,2,1] => [[1,5,7,8],[2,6],[3],[4]] => 4
[1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => [5,6,7,8,4,3,2,1] => [[1,6,7,8],[2],[3],[4],[5]] => 5
[1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => 2
[1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => [6,7,8,9,10,5,4,3,2,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 6
[1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => 2
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 first entry in the last row of a standard tableau.
For the last entry in the first row, see St000734The last entry in the first row of a standard tableau..
Map
non-nesting-exceedence permutation
Description
The fixed-point-free permutation with deficiencies given by the perfect matching, no alignments and no inversions between exceedences.
Put differently, the exceedences form the unique non-nesting perfect matching whose openers coincide with those of the given perfect matching.
Map
to tunnel matching
Description
Sends a Dyck path of semilength n to the noncrossing perfect matching given by matching an up-step with the corresponding down-step.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.
Map
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.