The partially finished new holonomy engine in SgpDec is chugging along well. This is the graph of the extended image set of the full transformation semigroup on four points, T4. This 'action graph' is like a Cayley-graph of the semigroup, but on the extended set of images rather than on the semigroup elements. The generators are the 'usual' ones:
- cycle: Transformation( [ 2, 3, 4, 1 ] )
- transposition: Transformation( [ 2, 1, 3, 4 ] )
- collapsing: Transformation( [ 1, 2, 3, 1 ] )
The number after the set in the label is the length of a minimal word needed to generate that particular set.
Legend:
ReplyDeleteNodes are members of the extended image set of the transformation semigroup, i.e. the full set, singletons, and subsets obtained by applying some word in generators to full set.
-labels on arrows are the corresponding generator
-target of an arrow is obtained by applying generator to each element of the source set
-arrows mapping a set to itself are not shown.
NB: these suppressed self arrows may permute the elements of the set in a non-trival way.