The graphical moves of projective conical spaces (II)

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.

new_colour_1

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.

new_colour_6

This is the projective version of the “mystery” move which appeared in the posts

Look at  the chemlambda DIST moves to see that this move is in the same family.

3. The R1 move.

new_colour_4

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.

new_colour_5This is a projective version of the GLC move R2 . The name comes from “Reidemeister 2” move.

5. The ext2 move.

new_colour_7This is a projective version of the GLC move ext2.

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!

_____________________________

Advertisements

4 thoughts on “The graphical moves of projective conical spaces (II)”

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s