Identifier
-
Mp00283:
Perfect matchings
—non-nesting-exceedence permutation⟶
Permutations
St000222: Permutations ⟶ ℤ
Values
[(1,2)] => [2,1] => 0
[(1,2),(3,4)] => [2,1,4,3] => 2
[(1,3),(2,4)] => [3,4,1,2] => 0
[(1,4),(2,3)] => [3,4,2,1] => 1
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => 6
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => 4
[(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => 5
[(1,5),(2,3),(4,6)] => [3,5,2,6,1,4] => 3
[(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => 4
[(1,6),(2,4),(3,5)] => [4,5,6,2,3,1] => 2
[(1,5),(2,4),(3,6)] => [4,5,6,2,1,3] => 1
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => 0
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => 2
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => 4
[(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => 5
[(1,3),(2,6),(4,5)] => [3,5,1,6,4,2] => 3
[(1,4),(2,6),(3,5)] => [4,5,6,1,3,2] => 1
[(1,5),(2,6),(3,4)] => [4,5,6,3,1,2] => 2
[(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => 3
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
Description
The number of alignments in the permutation.
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.
Put differently, the exceedences form the unique non-nesting perfect matching whose openers coincide with those of the given perfect matching.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!