SSL Minutes

8 Feb 2001
Abe & Nick

Geir brings beverages next time.

Abe S. and Nick P. took notes.

There was an error on pg 13 of "Generalized Domino Shuffling." The Fortress, which is labeled order 3 is actually order 4.

A point on rules of order: We should be patient in answering questions so that a higher proportion of the group can absorb and contemplate the questions. There's no reason anyone should get lost. Also, keep anecdotes under control.

Next Thursday or the Thursday after, Jim will meet with us one-on-one.

Also, as for the time sheets, hours are like electrons: i.e., indistinguishable. It doesn't matter to Jim what you right on the sheets as long as the total number of hours is correct.

We will be put on Domino and Bilinear email lists.

We were given a handout. We should be able to read sections 1,2,3,6,7,8 reasonably well.

Regions With Holes:

Take a 6x6 square with the middle 2x2 hole missing.

The height function is definable as long as the missing region is tileable. However, 2x2 block rotations can not be used to change the tile configuration.

David Wilson has done work on Aztec Windows. Search for it if you are interested.


Abe (me) discussed his (partial) solution for counting the tilings of a 2xn rectangle with exactle k verticle tiles. He noted that N(n,k)=N(n-1,k-1)+N(n-2,k)

By using induction on N and K, the following formula can be found: N(n,k) = C( n+k/2, k); where C(a,b) is the binomial coefficient (combination) function.

New Stuff:

Counting lozenge tilings on a semi-regular hexagon, sides of length a,b,c.

The number of tilings, H(a,b,c) = Product_{i=1..a, j=1..b, k=1..c} ((i+j+k-1)/(i+j+k-2))

New Homework:
1. Prove that H(a,b,1)=C(a+b, a) (i.e., (a+b)!/(a!b!) )
2. Use domino Shuffling to prove that H(2,2,2)=20.


Undergraduate Research Seminar volounteers: Kristin, Rachel, Nick?, Abe?, Pavle

As for X-forwarding in B107, we don't know how to fix it.

That is all!