This is a sage code which computes a kamma map for a finite semidistributive lattice, which is a bijection from the set of join-irreducible elements to that of meet-irreducible ones.
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"""A finite lattice is congruence-uniform (CU) if and only if it is constructed from a singleton | |
by iterating Day's doubling construction by intervals. | |
Using this fact, we can create a generator `CU_lattices_generator` | |
which yields finite CU lattices. | |
- Lattices appear without repetition (up to isomorphism), | |
- Every finite CU lattice appears by finitely many iterations. | |
""" | |
from collections import deque | |
singleton = LatticePoset({0: []}) |