Identifier
-
Mp00092:
Perfect matchings
—to set partition⟶
Set partitions
Mp00174: Set partitions —dual major index to intertwining number⟶ Set partitions
St000247: Set partitions ⟶ ℤ
Values
[(1,2)] => {{1,2}} => {{1,2}} => 0
[(1,2),(3,4)] => {{1,2},{3,4}} => {{1,2,4},{3}} => 1
[(1,3),(2,4)] => {{1,3},{2,4}} => {{1,4},{2,3}} => 0
[(1,4),(2,3)] => {{1,4},{2,3}} => {{1,3,4},{2}} => 1
[(1,2),(3,4),(5,6)] => {{1,2},{3,4},{5,6}} => {{1,2,4},{3,6},{5}} => 1
[(1,3),(2,4),(5,6)] => {{1,3},{2,4},{5,6}} => {{1,4},{2,3,6},{5}} => 1
[(1,4),(2,3),(5,6)] => {{1,4},{2,3},{5,6}} => {{1,3,4},{2,6},{5}} => 1
[(1,5),(2,3),(4,6)] => {{1,5},{2,3},{4,6}} => {{1,3},{2,6},{4,5}} => 0
[(1,6),(2,3),(4,5)] => {{1,6},{2,3},{4,5}} => {{1,3},{2,5,6},{4}} => 1
[(1,6),(2,4),(3,5)] => {{1,6},{2,4},{3,5}} => {{1,5,6},{2,4},{3}} => 1
[(1,5),(2,4),(3,6)] => {{1,5},{2,4},{3,6}} => {{1,6},{2,4,5},{3}} => 1
[(1,4),(2,5),(3,6)] => {{1,4},{2,5},{3,6}} => {{1,6},{2,5},{3,4}} => 0
[(1,3),(2,5),(4,6)] => {{1,3},{2,5},{4,6}} => {{1,6},{2,3,5},{4}} => 1
[(1,2),(3,5),(4,6)] => {{1,2},{3,5},{4,6}} => {{1,2,6},{3,5},{4}} => 1
[(1,2),(3,6),(4,5)] => {{1,2},{3,6},{4,5}} => {{1,2,5},{3},{4,6}} => 1
[(1,3),(2,6),(4,5)] => {{1,3},{2,6},{4,5}} => {{1,5},{2,3},{4,6}} => 0
[(1,4),(2,6),(3,5)] => {{1,4},{2,6},{3,5}} => {{1,5},{2},{3,4,6}} => 1
[(1,5),(2,6),(3,4)] => {{1,5},{2,6},{3,4}} => {{1,4,5},{2},{3,6}} => 1
[(1,6),(2,5),(3,4)] => {{1,6},{2,5},{3,4}} => {{1,4},{2},{3,5,6}} => 1
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Description
The number of singleton blocks of a set partition.
Map
dual major index to intertwining number
Description
A bijection sending the dual major index of a set partition to its intertwining number.
More precisely, St000493The los statistic of a set partition.$(P) = $St000490The intertwining number of a set partition.$(\phi(P))$ for all set partitions $P$.
This is the inverse of Mp00171intertwining number to dual major index.
More precisely, St000493The los statistic of a set partition.$(P) = $St000490The intertwining number of a set partition.$(\phi(P))$ for all set partitions $P$.
This is the inverse of Mp00171intertwining number to dual major index.
Map
to set partition
Description
Return the set partition corresponding to the perfect matching.
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