## A Gray Code for the Ideals of Acyclic Posets

(Enumerating Spider Squishings)

*Gang Li*, Department of Computer Science, University of Victoria.

*Frank Ruskey*, Department of Computer Science, University of Victoria.

Comments:
- These results were presented at the 26th South East Conference on
Combinatorics, Graph Theory, and Computing, 1995.
Here are some scans of the slides from that talk:

Slide #1
Title slide.

Slide #2
Background.

Slide #3
A six element fence poset and its ideal graph.

Slide #4
Spider = ayclic poset.

Slide #5
Spider for overlay.
(Slide #5'
Another spider.)

Slide #6
(Slide #6')
Spider = ayclic poset OVERLAY. Missing is a shoe
overlay for showing some squishings (something like
this and
this).

Slide #7a
Slide #7b
Slide #7c
Spider close-ups showing continued branching.

Slide #8
Parity difference is one of +1, 0, -1.

Slide #9
Definitions; e.g., *q*-code, squishings.

Slide #10
Allowed relations between *q* and *r*.

Slide #11
The path traced out by the proof and by the algorithm.

Slide #12
The relation between the proof and the algorithm.

Slide #13
Non-recursive look at the algorithm.

Slide #14
Second problem --- which ideal is first?

Slide #15
Final slide: Open Questions.

- Gang (Kenny) Li now works for i2 Technologies in Dallas, Texas.
- Donald Knuth liked the Gray code so much that he couldn't resist
developing his own implementation.
See his CWEB program
LI-RUSKEY .

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