kigen.chain-sgp — kigen 19.08.05

Chain semigroups based on a skeleton.

->chain-transf clj

(->chain-transf {hd :supsethd X :stateset} chains t)

A transformation encoding the action of a transformation on all maximal chains.

chain-sgp-gens clj

(chain-sgp-gens gens)

Just a convenient function to map generators to chain semigroup generators.

chain-transf-> clj

(chain-transf-> {X :stateset} chains c-t)

Taking a lift (a transformation of the set of chains) it gives back the original transformation.

check-morphism clj

(check-morphism gens)

Takes a generator set of transformations, produces a chain semigroup and checks the morphic relation by checking all products.

fillings clj

(fillings chains fullhd)

A map that contains filling for gaps in a reduced Hasse diagrams. Used for finding dominating chains.

gap? clj

(gap? a b hd)

Returns true if there is a gap between a and b in Hasse diagram hd, i.e. a is only transitively related to b.

gaps clj

(gaps chains fullhd)

Returns all pairs in the reduced cover relation that are not related in the full relation. Chains have to be given since BECKS produces examples where [0 1 3 3] where filling the gaps in the reduced hd is not enough!

max-chains clj

(max-chains X hd)

All maximal chains in an inclusion Hasse diagram hd with top set X.

on-hd clj

(on-hd hd X transf)

The result of acting by a transformation on superset Hasse diagram in a skeleton. The full state set and the singletons are put back.

on-max-chain clj

(on-max-chain c t fllngs)

Acting on maximal chain. Finding a dominating chain by using a fillings table.