SSL Minutes for Thursday, Nov. 6, 2003
Note-taker:  Paul
Snacks: Abby

Note taker for Tuesday: Martin
Snacks for Tuesday: Sam

Hal: It's Grunt.

Jim: I want to meet you all individually on Tuesday. (Assigns times for the meetings)
Jim: Instead of attatching documents to emails to ssl, just put a link in an email to 
the place on your website where we can find it.
Paul: Geocities will not allow for .mws uploads
Jim, Hal and Jon talk about asking Yvonne to allow our accounts the ability to create 
webpages through undergrad.math.wisc.edu.

Jim: One of the top level goals in SSL is to understand Somos and Somos-like sequences
and what they might have to do with combinatorial objects.  We want to answer questions
like: Can "cube snakes" or appolonian gaskets illuminate anything about Somos or 
Somos-like sequences?
Enter Scott Scheffield.
Jim: If anyone doesnt have graph.tcl, they should get it, as it makes large graphs not
so tedious.  Lets go around and see what everyone has been doing since Tuesday.

Hal: I haven't done much in terms of SSL since Tuesday.
Carl: Played with the bijection between even 2 x 2 x n perfect matchings and ordered 
pairs of 3 x 2n domino tilings.  Also, looked further into "face matchings".
Stephen: Looking at small examples of cluster algebras.
Jim: For an example of what we should look for in SSL, double wiring schemes give 
Laurent polynomials where every coefficient is + or - 1.  Could we describe what 
type of monomials occur?
Stephen: Only one dimensional cluster algebra that I know of is the universal degree 
2 with the real line and points that are integers.
Abby: Read Carls face matching text and Pauls generating function text.  Independently 
reproduced it for odd number of cubes.
Jon: Talked with Carl and Paul after the last meeting about odd cubes and 3 x 2n 
bijection.
Emilie: Looking at equations of rational solutions to Jims question about polygonal 
diagonals and getting somwhere until the variable of interest disappeared.
Jim: I'll talk to M. Isaacs about it.
Martin: Trying to read a book on automata, but very algebraic and I dont know if I 
can get through it.
Jim: We should take a look at the odd cube polynomials and see if their square roots 
follow a linear recurrence. Suppose we have a sequence a(1), a(2), a(3), a(4), a(5), 
a(6)...
Then the matrix (a(1) a(2) a(3))
                (a(2) a(3) a(4))
                (a(3) a(4) a(5))
has a nonzero determinant only if it does not follow a second order linear recurrence, 
since if it nonsingular it has no nontrivial solutions of 

                (a(1) a(2) a(3)) ( A )   (0)
                (a(2) a(3) a(4)) ( B ) = (0)
                (a(3) a(4) a(5)) (-1 )   (0).

Lets take a break to eat.
(Move to B107, and everyone uses Maple to look at different things)

End Meeting.