Wk 6, Tu

Brussel sprouts and lima beans! There are less than 3 weeks left!

Progress, progress... I proved that given a configuration m#(a,b,c,d,b,a,d,c), it has complements m#(b,c,a,d,c,b,d,a) and m#(c,a,b,d,a,c,d,b). Now I'm trying to generalize this.

After a questionable proof and a feeble attempt at coding, I discovered a pair of nontrivial configurations that trivially satisfied the conditions for being superimposable/having extra intersections!

Furthermore, while my code yields non-realizable configurations (i.e., useless), it still (I think) shows where it's not possible, and I think I'm finding a correlation:

1. According to my code (and my analysis of the results it yielded), there are NO superimposable configurations for m = 8, 9, 10, 11, 13, 14, 16, 17, 19, or 20 (15 is questionable: it was too extensive to check according to one coding [this code was yielding pattern 2 cfgs, which was way bad], and the second coding of restrictions said there were none. so, it's very, very unlikely that there are any superimposable cfgs for m=15).

2. Conjecture: a configuration is superimposable if it is half-trivial, i.e., two elements of S are the same as two elements of T.
*I'm having a little bit of trouble determining the direction of this implication, so:

3. According to Angela's data, there are no half-trivial configurations for m = 8, 9, 10, 11, 13, 14, 15, 16, 17, or 19, (haven't checked 20 yet) but there IS one in 12, which just so happens to yield the two pairs of superimposables.

Wk 5, M

8:30-11
2-3
10-11

i have two pages of notes trying to figure out how to generalize my theorem! geeze!

Wk 4, Th

9-11:30 -- paper revisions; 6-celestial pre-work
1:30-3 -- made a (3,4) cfg
3-4 -- 6-celestial exps

Wk 4, W

7:20am-9 -- typed paper
9-10 -- meeting
10-11:30 -- surfed and slept
11:30-12 -- configured
2-3 -- i think i was working on categorizing the properties?

i was up at 6 this morning! how have i only worked 4 hours?!

Wk 3, F

8:30-9:30--"finished" proof, i.e., wrote up angle problem solution
9:30-10:30--meeting w/berman
10:30... added more pictures to paper

Wk 3, Th

9-12 -- wrote half a page; other half of page: picture
12-3:30 -- lunch, talk, tutored
3:30-5:30 -- papered
6-7-- papered futile-y

i hate papers.

Wk 3, Tu

9:30-11 -- tried to fix "101 error(s)" in Latex in my tables (i was missing some dollar signs)
i was wondering about formatting. how do my tables look? (i was also thinking they could be equation lists, like to show the middle step, and forget about having columns.
1-2:30 -- worked on showing (and typing up) that the angles must be the same. got half way there.
i think this also leads to some interesting questions about configurations... i wonder if anyone's done any research on the placement of vertices? (especially with the pairing that occurs with trivial configurations). for instance, when are the symmetry classes of points collinear?
2:30-3:30 -- outlined proof, for organizational purposes; blogged.
11-12 -- reviewed proof for tomorrow

today, like yesterday, was very much a writing day.