Continues from The graphical moves of projective conical spaces (I).
In this post we see the list of moves.
The colours X and O are added to show that the moves preserve the class of graphs PROJGRAPH.
The drawing convention is the following: columns of colours represent possible different choices of colouring. In order to read correctly the choices, one should take, for example, the first elements from all columns, as a choice, then the second element from all columns, etc. When there is only one colour indicated, in some places, then there is only one choice for the respective arrow. Finally, I have not added symmetric choices obtained by replacing everywhere X by O and O by X.
1. The PG move.
As you see, there is only one PG move. There are 3 different choices of colours, which results into 3 versions of the PG move, as explained in the post A simple explanation with types of the hexagonal moves of projective spaces.
2. The DIST move.
This is the projective version of the “mystery” move which appeared in the posts
- Dictionary from emergent algebra to graphic lambda calculus (I)
- Dictionary from emergent algebra to graphic lambda calculus (II)
- Dictionary from emergent algebra to graphic lambda calculus (III)
Look at the chemlambda DIST moves to see that this move is in the same family.
3. The R1 move.
This is a projective version of the GLC move R1 (more precisely R1a). The name comes from “Reidemeister 1” move, as seen through the lens of emergent algebras.
4. The R2 move.
This is a projective version of the GLC move R2 . The name comes from “Reidemeister 2” move.
5. The ext2 move.
6. CO-COMM, CO-ASSOC and LOC PRUNING. These are the usual moves associated to the fanout node. The LOC PRUNING move for the dilation node is also clear.
All these moves are local!