Identifier
Values
=>
Cc0012;cc-rep-0 Cc0009;cc-rep
[(1,2)]=>{{1,2}}=>0 [(1,2),(3,4)]=>{{1,2},{3,4}}=>0 [(1,3),(2,4)]=>{{1,3},{2,4}}=>1 [(1,4),(2,3)]=>{{1,4},{2,3}}=>2 [(1,2),(3,4),(5,6)]=>{{1,2},{3,4},{5,6}}=>0 [(1,3),(2,4),(5,6)]=>{{1,3},{2,4},{5,6}}=>1 [(1,4),(2,3),(5,6)]=>{{1,4},{2,3},{5,6}}=>2 [(1,5),(2,3),(4,6)]=>{{1,5},{2,3},{4,6}}=>3 [(1,6),(2,3),(4,5)]=>{{1,6},{2,3},{4,5}}=>4 [(1,6),(2,4),(3,5)]=>{{1,6},{2,4},{3,5}}=>5 [(1,5),(2,4),(3,6)]=>{{1,5},{2,4},{3,6}}=>4 [(1,4),(2,5),(3,6)]=>{{1,4},{2,5},{3,6}}=>3 [(1,3),(2,5),(4,6)]=>{{1,3},{2,5},{4,6}}=>2 [(1,2),(3,5),(4,6)]=>{{1,2},{3,5},{4,6}}=>1 [(1,2),(3,6),(4,5)]=>{{1,2},{3,6},{4,5}}=>2 [(1,3),(2,6),(4,5)]=>{{1,3},{2,6},{4,5}}=>3 [(1,4),(2,6),(3,5)]=>{{1,4},{2,6},{3,5}}=>4 [(1,5),(2,6),(3,4)]=>{{1,5},{2,6},{3,4}}=>5 [(1,6),(2,5),(3,4)]=>{{1,6},{2,5},{3,4}}=>6
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Description
The number of inversions of a set partition.
The Mahonian representation of a set partition $\{B_1,\dots,B_k\}$ of $\{1,\dots,n\}$ is the restricted growth word $w_1\dots w_n\}$ obtained by sorting the blocks of the set partition according to their maximal element, and setting $w_i$ to the index of the block containing $i$.
A pair $(i,j)$ is an inversion of the word $w$ if $w_i > w_j$.
Map
to set partition
Description
Return the set partition corresponding to the perfect matching.