Identifier
Values
[1,0] => [(1,2)] => {{1,2}} => 0
[1,0,1,0] => [(1,2),(3,4)] => {{1,2},{3,4}} => 0
[1,1,0,0] => [(1,4),(2,3)] => {{1,4},{2,3}} => 2
[1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => {{1,2},{3,4},{5,6}} => 0
[1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => {{1,2},{3,6},{4,5}} => 2
[1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => {{1,4},{2,3},{5,6}} => 2
[1,1,0,1,0,0] => [(1,6),(2,3),(4,5)] => {{1,6},{2,3},{4,5}} => 4
[1,1,1,0,0,0] => [(1,6),(2,5),(3,4)] => {{1,6},{2,5},{3,4}} => 6
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Description
The number of occurrences of the pattern {{1,3},{2}} in a set partition.
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
to set partition
Description
Return the set partition corresponding to the perfect matching.