20 March 2001
(someone?) is working on proving that the larger matrix in the ASM representation of an order "2" (n) aztec diamond is the smaller matrix in the order "3" (n+1) ASM after doing domino shuffling.
Jim pointed out that "pushing down" the height in an aztec diamond is equivalant to adding [1, -1; -1, 1] to the ASM.
(Hal) proposed the idea of looking at ASM hieght functions with the minimum height fuction subtracted out of them to see if the properties were interesting.
Some ideas for the fair were tossed around, including displaying Hal's java program, and explaining various things we're working on, such as the Baxter conjecture and the blue-green model conjecture.
Jim explained one of the properties of compatable ASM pairs. Each ASM is compatable with 2**[number of -1s] smaller ASMs and 2**[number of 1s] larger ASMs. Each item can be represented as one item in an ordered postset, where each order of ASM represents one level of depth. By taking a random path from the bottom up you can generate a random pair of compatable ASMs. However, you need to use some sort of weighting to generate a random ASM because picking a random path will favor ASMs with more -1s
Geir showed that you can quickly convert between an ASM to a densely packed flux line model by going straight on 0 and turning on -1/1