Identifier
Mp00092: Perfect matchings —to set partition⟶ Set partitions
Mp00115: Set partitions —Kasraoui-Zeng⟶ Set partitions
Mp00258: Set partitions —Standard tableau associated to a set partition⟶ Standard tableaux
Images
=>
Cc0012;cc-rep-0Cc0009;cc-rep-1Cc0009;cc-rep-2Cc0007;cc-rep-3
[(1,2)]=>{{1,2}}=>{{1,2}}=>[[1,2]] [(1,2),(3,4)]=>{{1,2},{3,4}}=>{{1,2},{3,4}}=>[[1,2],[3,4]] [(1,3),(2,4)]=>{{1,3},{2,4}}=>{{1,4},{2,3}}=>[[1,3],[2,4]] [(1,4),(2,3)]=>{{1,4},{2,3}}=>{{1,3},{2,4}}=>[[1,3],[2,4]] [(1,2),(3,4),(5,6)]=>{{1,2},{3,4},{5,6}}=>{{1,2},{3,4},{5,6}}=>[[1,2],[3,4],[5,6]] [(1,3),(2,4),(5,6)]=>{{1,3},{2,4},{5,6}}=>{{1,4},{2,3},{5,6}}=>[[1,3],[2,4],[5,6]] [(1,4),(2,3),(5,6)]=>{{1,4},{2,3},{5,6}}=>{{1,3},{2,4},{5,6}}=>[[1,3],[2,4],[5,6]] [(1,5),(2,3),(4,6)]=>{{1,5},{2,3},{4,6}}=>{{1,3},{2,6},{4,5}}=>[[1,3],[2,5],[4,6]] [(1,6),(2,3),(4,5)]=>{{1,6},{2,3},{4,5}}=>{{1,3},{2,5},{4,6}}=>[[1,3],[2,5],[4,6]] [(1,6),(2,4),(3,5)]=>{{1,6},{2,4},{3,5}}=>{{1,5},{2,4},{3,6}}=>[[1,4],[2,5],[3,6]] [(1,5),(2,4),(3,6)]=>{{1,5},{2,4},{3,6}}=>{{1,6},{2,4},{3,5}}=>[[1,4],[2,5],[3,6]] [(1,4),(2,5),(3,6)]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}}=>[[1,4],[2,5],[3,6]] [(1,3),(2,5),(4,6)]=>{{1,3},{2,5},{4,6}}=>{{1,6},{2,3},{4,5}}=>[[1,3],[2,5],[4,6]] [(1,2),(3,5),(4,6)]=>{{1,2},{3,5},{4,6}}=>{{1,2},{3,6},{4,5}}=>[[1,2],[3,5],[4,6]] [(1,2),(3,6),(4,5)]=>{{1,2},{3,6},{4,5}}=>{{1,2},{3,5},{4,6}}=>[[1,2],[3,5],[4,6]] [(1,3),(2,6),(4,5)]=>{{1,3},{2,6},{4,5}}=>{{1,5},{2,3},{4,6}}=>[[1,3],[2,5],[4,6]] [(1,4),(2,6),(3,5)]=>{{1,4},{2,6},{3,5}}=>{{1,5},{2,6},{3,4}}=>[[1,4],[2,5],[3,6]] [(1,5),(2,6),(3,4)]=>{{1,5},{2,6},{3,4}}=>{{1,4},{2,6},{3,5}}=>[[1,4],[2,5],[3,6]] [(1,6),(2,5),(3,4)]=>{{1,6},{2,5},{3,4}}=>{{1,4},{2,5},{3,6}}=>[[1,4],[2,5],[3,6]]
Map
to set partition
Description
Return the set partition corresponding to the perfect matching.
Map
Kasraoui-Zeng
Description
The Kasraoui-Zeng involution.
This is defined in [1] and yields the set partition with the number of nestings and crossings exchanged.
Map
Standard tableau associated to a set partition
Description
Sends a set partition to the associated standard tableau.
The $j$th column of the standard tableau associated to a set partition is the set of $j$th smallest elements of its blocks arranged in increassing order.