**On my wish list is to have a java applet for Groves on standard initials
similar to this
one for Aztec Diamonds.**

**I've written some code for maple that draws pretty pictures of groves.
I think the algorithm is implementable for java if anyone wants to translate
it. Look Here for a picture of a big random
grove and my maple code.**

**I gave a talk at Brandeis on March 12, 2003 about asymptotic behavior
in groves. Here is my powerpoint presentation.**

**Here is a very rough draft of an arctic circle paper I'm writing
with David Speyer:**

**Here are some pictures of some (small) random groves on standard
initial conditions. Print them out and color away!**

**During fall of 2002 I worked on monomer-dimer tilings with
John Baldwin,
Nick Anzalone, and
Ilya Bronshtein.**

**Some preliminary results for the monomer-dimer
question. If you don't have Flash Player, you can download
it here.**

**Here is some maple code that I wrote in early investigations.
Save the files below and open them with maple.**

For 2 by n rectangles (weights on edges only)

For 1 by n and 2 by n (weights on edges and vertices)

**The updated version of the formal paper on monomer-dimer tilings,
titled "A reciprocity theorem for monomer-dimer coverings" is below.
The version below was last updated on April 14.**

source(LaTeX) bibliography figures: mondim1.epsmondim2.epsmondim3.epsmondim4.epsmondim5.epsmondim6.epsmondim7.epsmondim8.epsmondim9.epsmondim10.epsmondim11.eps

**A fun question (is there some math here?):**

**Play the game "Pile
Up" five times in a row by only pushing the spacebar. Did you
always get past the first level? The board has height 16 and width
8. There are five colors of balls, presented randomly in groups of
three and dropped down the center of the board. The balls stack on
top of one another in the natural way (some randomness is involved when
a ball can fall to the left or right). If four or more balls of the
same color are connected, then they are removed from the board and the
remaining balls fall to fill the space. The first level is completed
when a cumulative total of 80 balls are removed from the board. What
is the probability of success when using the 'spacebar' strategy?**