Last Update: May 19, 2009.
The Gambler's Ruin problem can be viewed as random walk in the fixed interval on the discrete line segment [0,A]. Study, both by simulation, and by symbol-crunching walks in the 2D lattice with unit steps in the four fundamental directions where you start at (x,y) travel in [0,A]x[0,B] and get kicked out as soon as you hit one of the walls x=0,x=A,y=0,y=B. This is very hard, so how about fix B to be numeric (B=1,2,3, etc.) but keep A symbolic. [Claimed by Liyang Diao]. Here is Liyang Diao's projet (preliminary version).
Studying the Cayley graph of Thompson's Group F.
[Claimed by Andrew Baxter and Dan Staley, and suggested by them].
Last update May 19, 2009: Here is Dan Staley and Andrew Baxter's Maple package, and here is some auxilary file, and Maple worksheet.
Study experimentally/symbolically Percolation in a strip. [Kellen Myers and Robert DeMarco]. Here is a preliminary version of Kellen and Bobby's project. It would hopefully be replaced by a final version.
Study expermintally/symbolically the Ising Model with a magnetic field in a finite-width infinite strip. [Claimed by Dennis Hou] . Coming Up.
Make the program gSAW(n,a,b,c,d,PAT) from Mar9.txt much more efficient, and experiment with many a,b,c,d, PAT, to get sequences with θ that are not zero. Possibly using the method of this paper, or more systematically that paper, teach the computer how to find closed form rational generating functions with finite a and b but c=-infinity, d=infinity. [Claimed by Brian Nakamura, and (possibly). Jeffrey Amos] Coming Up.