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.