- FindStat

edit this map or download as text // json

Identifier

Mp00220: Set partitions —Yip⟶ Set partitions

Images

{} => {}

{{1}} => {{1}}

{{1,2}} => {{1,2}}

{{1},{2}} => {{1},{2}}

{{1,2,3}} => {{1,2,3}}

{{1,2},{3}} => {{1,2},{3}}

{{1,3},{2}} => {{1},{2,3}}

{{1},{2,3}} => {{1,3},{2}}

{{1},{2},{3}} => {{1},{2},{3}}

{{1,2,3,4}} => {{1,2,3,4}}

{{1,2,3},{4}} => {{1,2,3},{4}}

{{1,2,4},{3}} => {{1,2},{3,4}}

{{1,2},{3,4}} => {{1,2,4},{3}}

{{1,2},{3},{4}} => {{1,2},{3},{4}}

{{1,3,4},{2}} => {{1},{2,3,4}}

{{1,3},{2,4}} => {{1,4},{2,3}}

{{1,3},{2},{4}} => {{1},{2,3},{4}}

{{1,4},{2,3}} => {{1,3},{2,4}}

{{1},{2,3,4}} => {{1,3,4},{2}}

{{1},{2,3},{4}} => {{1,3},{2},{4}}

{{1,4},{2},{3}} => {{1},{2},{3,4}}

{{1},{2,4},{3}} => {{1},{2,4},{3}}

{{1},{2},{3,4}} => {{1,4},{2},{3}}

{{1},{2},{3},{4}} => {{1},{2},{3},{4}}

{{1,2,3,4,5}} => {{1,2,3,4,5}}

{{1,2,3,4},{5}} => {{1,2,3,4},{5}}

{{1,2,3,5},{4}} => {{1,2,3},{4,5}}

{{1,2,3},{4,5}} => {{1,2,3,5},{4}}

{{1,2,3},{4},{5}} => {{1,2,3},{4},{5}}

{{1,2,4,5},{3}} => {{1,2,5},{3,4}}

{{1,2,4},{3,5}} => {{1,2},{3,4,5}}

{{1,2,4},{3},{5}} => {{1,2},{3,4},{5}}

{{1,2,5},{3,4}} => {{1,2,4},{3,5}}

{{1,2},{3,4,5}} => {{1,2,4,5},{3}}

{{1,2},{3,4},{5}} => {{1,2,4},{3},{5}}

{{1,2,5},{3},{4}} => {{1,2},{3},{4,5}}

{{1,2},{3,5},{4}} => {{1,2},{3,5},{4}}

{{1,2},{3},{4,5}} => {{1,2,5},{3},{4}}

{{1,2},{3},{4},{5}} => {{1,2},{3},{4},{5}}

{{1,3,4,5},{2}} => {{1},{2,3,4,5}}

{{1,3,4},{2,5}} => {{1,5},{2,3,4}}

{{1,3,4},{2},{5}} => {{1},{2,3,4},{5}}

{{1,3,5},{2,4}} => {{1,4},{2,3,5}}

{{1,3},{2,4,5}} => {{1,4,5},{2,3}}

{{1,3},{2,4},{5}} => {{1,4},{2,3},{5}}

{{1,3,5},{2},{4}} => {{1,5},{2,3},{4}}

{{1,3},{2,5},{4}} => {{1},{2,3},{4,5}}

{{1,3},{2},{4,5}} => {{1},{2,3,5},{4}}

{{1,3},{2},{4},{5}} => {{1},{2,3},{4},{5}}

{{1,4,5},{2,3}} => {{1,3,5},{2,4}}

{{1,4},{2,3,5}} => {{1,3},{2,4,5}}

{{1,4},{2,3},{5}} => {{1,3},{2,4},{5}}

{{1,5},{2,3,4}} => {{1,3,4},{2,5}}

{{1},{2,3,4,5}} => {{1,3,4,5},{2}}

{{1},{2,3,4},{5}} => {{1,3,4},{2},{5}}

{{1,5},{2,3},{4}} => {{1,3},{2},{4,5}}

{{1},{2,3,5},{4}} => {{1,3},{2,5},{4}}

{{1},{2,3},{4,5}} => {{1,3,5},{2},{4}}

{{1},{2,3},{4},{5}} => {{1,3},{2},{4},{5}}

{{1,4,5},{2},{3}} => {{1},{2},{3,4,5}}

{{1,4},{2,5},{3}} => {{1},{2,5},{3,4}}

{{1,4},{2},{3,5}} => {{1,5},{2},{3,4}}

{{1,4},{2},{3},{5}} => {{1},{2},{3,4},{5}}

{{1,5},{2,4},{3}} => {{1},{2,4},{3,5}}

{{1},{2,4,5},{3}} => {{1},{2,4,5},{3}}

{{1},{2,4},{3,5}} => {{1,5},{2,4},{3}}

{{1},{2,4},{3},{5}} => {{1},{2,4},{3},{5}}

{{1,5},{2},{3,4}} => {{1,4},{2},{3,5}}

{{1},{2,5},{3,4}} => {{1,4},{2,5},{3}}

{{1},{2},{3,4,5}} => {{1,4,5},{2},{3}}

{{1},{2},{3,4},{5}} => {{1,4},{2},{3},{5}}

{{1,5},{2},{3},{4}} => {{1},{2},{3},{4,5}}

{{1},{2,5},{3},{4}} => {{1},{2},{3,5},{4}}

{{1},{2},{3,5},{4}} => {{1},{2,5},{3},{4}}

{{1},{2},{3},{4,5}} => {{1,5},{2},{3},{4}}

{{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}}

{{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}

{{1,2,3,4,5},{6}} => {{1,2,3,4,5},{6}}

{{1,2,3,4,6},{5}} => {{1,2,3,4},{5,6}}

{{1,2,3,4},{5,6}} => {{1,2,3,4,6},{5}}

{{1,2,3,4},{5},{6}} => {{1,2,3,4},{5},{6}}

{{1,2,3,5,6},{4}} => {{1,2,3,6},{4,5}}

{{1,2,3,5},{4,6}} => {{1,2,3},{4,5,6}}

{{1,2,3,5},{4},{6}} => {{1,2,3},{4,5},{6}}

{{1,2,3,6},{4,5}} => {{1,2,3,5},{4,6}}

{{1,2,3},{4,5,6}} => {{1,2,3,5,6},{4}}

{{1,2,3},{4,5},{6}} => {{1,2,3,5},{4},{6}}

{{1,2,3,6},{4},{5}} => {{1,2,3},{4},{5,6}}

{{1,2,3},{4,6},{5}} => {{1,2,3},{4,6},{5}}

{{1,2,3},{4},{5,6}} => {{1,2,3,6},{4},{5}}

{{1,2,3},{4},{5},{6}} => {{1,2,3},{4},{5},{6}}

{{1,2,4,5,6},{3}} => {{1,2,5,6},{3,4}}

{{1,2,4,5},{3,6}} => {{1,2,5},{3,4,6}}

{{1,2,4,5},{3},{6}} => {{1,2,5},{3,4},{6}}

{{1,2,4,6},{3,5}} => {{1,2,6},{3,4,5}}

{{1,2,4},{3,5,6}} => {{1,2},{3,4,5,6}}

{{1,2,4},{3,5},{6}} => {{1,2},{3,4,5},{6}}

{{1,2,4,6},{3},{5}} => {{1,2},{3,4,6},{5}}

{{1,2,4},{3,6},{5}} => {{1,2},{3,4},{5,6}}

{{1,2,4},{3},{5,6}} => {{1,2,6},{3,4},{5}}

{{1,2,4},{3},{5},{6}} => {{1,2},{3,4},{5},{6}}

>>> Load all 6680 entries. <<<

click to show experimental identities (only identities of compositions of up to three maps are shown)

Description

A transformation of set partitions due to Yip.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Yip's bijection $\psi$.

References

[1] Yip, M. Rook placements and Jordan forms of upper-triangular nilpotent matrices MathSciNet:3799468

Properties

bijective, graded

Sage code

def mapping(p):
    return SetPartitions(p.size()).from_rook_placement(p.to_rook_placement("arcs"), "psi")

Weight

Created

Feb 27, 2021 at 19:21 by Martin Rubey

Updated

Feb 27, 2021 at 19:21 by Martin Rubey