Identifier
Values
[(1,2),(3,4),(5,6)] => [1,0,1,0,1,0] => [1,1,1] => [3] => 1
[(1,2),(3,4),(5,6),(7,8)] => [1,0,1,0,1,0,1,0] => [1,1,1,1] => [4] => 1
[(1,3),(2,4),(5,6),(7,8)] => [1,1,0,0,1,0,1,0] => [2,1,1] => [1,2] => 0
[(1,4),(2,3),(5,6),(7,8)] => [1,1,0,0,1,0,1,0] => [2,1,1] => [1,2] => 0
[(1,2),(3,5),(4,6),(7,8)] => [1,0,1,1,0,0,1,0] => [1,2,1] => [1,1,1] => 1
[(1,2),(3,6),(4,5),(7,8)] => [1,0,1,1,0,0,1,0] => [1,2,1] => [1,1,1] => 1
[(1,2),(3,4),(5,7),(6,8)] => [1,0,1,0,1,1,0,0] => [1,1,2] => [2,1] => 0
[(1,2),(3,4),(5,8),(6,7)] => [1,0,1,0,1,1,0,0] => [1,1,2] => [2,1] => 0
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => [5] => 1
[(1,3),(2,4),(5,6),(7,8),(9,10)] => [1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [1,3] => 0
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [1,3] => 0
[(1,5),(2,3),(4,6),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => [3,1,1] => [1,2] => 0
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => [3,1,1] => [1,2] => 0
[(1,6),(2,4),(3,5),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [1,2] => 0
[(1,5),(2,4),(3,6),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [1,2] => 0
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [1,2] => 0
[(1,3),(2,5),(4,6),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => [3,1,1] => [1,2] => 0
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [1,1,2] => 1
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [1,1,2] => 1
[(1,3),(2,6),(4,5),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => [3,1,1] => [1,2] => 0
[(1,4),(2,6),(3,5),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [1,2] => 0
[(1,5),(2,6),(3,4),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [1,2] => 0
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [1,2] => 0
[(1,2),(3,7),(4,5),(6,8),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => [1,3,1] => [1,1,1] => 1
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => [1,3,1] => [1,1,1] => 1
[(1,2),(3,8),(4,6),(5,7),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [1,1,1] => 1
[(1,2),(3,7),(4,6),(5,8),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [1,1,1] => 1
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [1,1,1] => 1
[(1,2),(3,5),(4,7),(6,8),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => [1,3,1] => [1,1,1] => 1
[(1,4),(2,3),(5,7),(6,8),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [2,1] => 0
[(1,3),(2,4),(5,7),(6,8),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [2,1] => 0
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => [2,1,1] => 1
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => [2,1,1] => 1
[(1,3),(2,4),(5,8),(6,7),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [2,1] => 0
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [2,1] => 0
[(1,2),(3,5),(4,8),(6,7),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => [1,3,1] => [1,1,1] => 1
[(1,2),(3,6),(4,8),(5,7),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [1,1,1] => 1
[(1,2),(3,7),(4,8),(5,6),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [1,1,1] => 1
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [1,1,1] => 1
[(1,2),(3,4),(5,9),(6,7),(8,10)] => [1,0,1,0,1,1,0,1,0,0] => [1,1,3] => [2,1] => 0
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [1,0,1,0,1,1,0,1,0,0] => [1,1,3] => [2,1] => 0
[(1,2),(3,4),(5,10),(6,8),(7,9)] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [2,1] => 0
[(1,2),(3,4),(5,9),(6,8),(7,10)] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [2,1] => 0
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [2,1] => 0
[(1,2),(3,4),(5,7),(6,9),(8,10)] => [1,0,1,0,1,1,0,1,0,0] => [1,1,3] => [2,1] => 0
[(1,2),(3,6),(4,5),(7,9),(8,10)] => [1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [1,2] => 0
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [1,2] => 0
[(1,4),(2,3),(5,6),(7,9),(8,10)] => [1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [1,1,1] => 1
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [1,1,1] => 1
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [3,1] => 0
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [3,1] => 0
[(1,3),(2,4),(5,6),(7,10),(8,9)] => [1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [1,1,1] => 1
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [1,1,1] => 1
[(1,2),(3,5),(4,6),(7,10),(8,9)] => [1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [1,2] => 0
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [1,2] => 0
[(1,2),(3,4),(5,7),(6,10),(8,9)] => [1,0,1,0,1,1,0,1,0,0] => [1,1,3] => [2,1] => 0
[(1,2),(3,4),(5,8),(6,10),(7,9)] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [2,1] => 0
[(1,2),(3,4),(5,9),(6,10),(7,8)] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [2,1] => 0
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [2,1] => 0
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => [1,1,1] => 1
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => [2,1,2] => 3
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => [2,2] => 1
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => [2,2] => 1
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => [3] => 1
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,4,1] => [1,1,1] => 1
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,3,1] => [2,1,1] => 1
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1] => [1,1,1] => 1
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4] => [2,1] => 0
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,1,1] => [1,1,2] => 1
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [1,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1] => [1,2] => 0
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2] => [1,1,1] => 1
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,4] => [2,1] => 0
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,1] => [1,2] => 0
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,1] => [1,1,1] => 1
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => [6] => 1
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => [1,4] => 0
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => [4,1] => 0
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => [1,2,1] => 2
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,4,1] => [1,1,1] => 1
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [2,1,1] => 1
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => [1,1,1] => 1
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4] => [2,1] => 0
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => [1,1,3] => 2
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1] => [1,3] => 0
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => [1,1,1,1] => 0
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,2] => [1,1,1] => 1
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4] => [2,1] => 0
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => [1,3] => 0
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => [1,1,1] => 1
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,1] => [1,1,1] => 1
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => [3,1,1] => 2
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => [1,1,1,1] => 0
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3] => [3,1] => 0
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3] => [1,1,1] => 1
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => [1,1,2] => 1
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [1,1,0,1,1,0,0,0,1,0,1,0] => [4,1,1] => [1,2] => 0
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => [1,1,1] => 1
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => [3,1] => 0
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,1] => [1,2] => 0
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => [1,1,1] => 1
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => [1,2,1] => 2
>>> Load all 107 entries. <<<
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [1,1,0,1,0,0,1,1,0,0,1,0] => [3,2,1] => [1,1,1] => 1
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3] => [1,1,1] => 1
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => [2,1] => 0
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => [1,1,1] => 1
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => [1,1,1] => 1
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => [1,2] => 0
search for individual values
searching the database for the individual values of this statistic
Description
The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles.
Map
to Dyck path
Description
The Dyck path corresponding to the opener-closer sequence of the perfect matching.
Map
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.