rowmotion for semidistributive lattices

[mantepse]

Problem Description

Given a semidistributive lattice L, rowmotion is an action on L. This should be a method of FiniteLatticePoset.

Proposed Solution

Here is the germ of an implementation due to Nathan Williams:

L=CoxeterGroup(['A',2]).weak_lattice()
lower=dict([(l,Set(L.canonical_joinands(l))) for l in L])
J=L.join_irreducibles()
M=L.meet_irreducibles()
meet_to_join=dict([(m,L.meet([l for l in J if L.le(l,L.upper_covers(m)[0]) and not(L.le(l,m))])) for m in M])
upper=dict([(Set([meet_to_join[i] for i in L.canonical_meetands(l)]),l) for l in L])
def semi_dist_row(l):
   return upper[lower[l]]
from sage.combinat.cyclic_sieving_phenomenon import *
list(map(len,orbit_decomposition(L,semi_dist_row)))

Alternatives Considered

na

Additional Information

No response

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