Updated Master Document

This version now contains the notation in the introduction and has the updated version of the 13 section using interiors of the triangular regions.

LaTeX, PDF

Something that occurred to me that we should consider: Should we write down what exactly are the 4 rigid transformations for regions III-VI (i.e., the rotations and translations) like I did in the exactly 1 section?

Updated 13 section

The solution we came up with for the P_I = P_III issue is that the cells (1,N) belongs to P_III but is not covered by the rigid transformation of the configuration in I shifted by (+1,-1). (Likewise for P_V.)

LaTeX

Draft of 1 or 3 figure

New revised figure draft for 1 or 3.

figure

Is this a reasonable format, or shall we do something different (keeping the paper cohesive)?

References

Also, please gather a preliminary list of references and add them as a final section in the main document.

Get to Work!

Charlie's post looks like a big improvement. I'll see the three of you on April 9. It would be great if a little more progress could transpire by then. For starters,

* a reasonably polished draft of the 14 section by Mike;
* a good start on the 134 material by Hannah;
* insertion of the Notation into the main document (including the new rotation notation).

Also, first drafts of the figures would be great.

Have a nice break,
D.

2 things to do / keep in mind

1. Delete unnecessary "rotated" throughout the document
2. Include periods, commas and semicolons in displays

1 or 3 triangle business

I think I got the triangle book-keeping down in a relatively neat fashion. It required some new notation (P_I for the population in region I, P_II for region II, etc.), but I think it's pretty slick in the end.

Master document: LaTeX, PDF

Suggested change: instead of

"we examine the six triangular regions and one square (see Fig. **) bounded by"

how about we delete the "bounded by" (it's awkward because we give region 7 as a Cartesian product) and change all the ='s to >='s in the description of each region.

Also, we need to add a paragraph to this section proving "no backfill."