Rui Viana - REACH 2002 |
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REACH = Research Experiences
in Algebraic Combinatorics at Harvard.

**Spotlight**:

- See the write-up of the article
on a Combinatorial Interpretation for the Markov Numbers

- See a descrition of the problem I am working on.

- Background:

+ The quadratic equation

+ The linear equation

+ Condensation

+ Cuts

- Right now there are
four proofs for this problem:

+ Proving the quadratic equation with
cuts

+ Proving the
linear equation with cuts

+ Proving the quadratic equation with
condensation theorems

+ Proving the linear equation with
condensation theorems

I have generated
some graphs
for the Markov n-tuples when n=4. This strongly suggests the existence
of these graphs, for any n.

Here are the files for the matchings applet I wrote: Matchings.class, Calculator.java, Edge.java, Grid.java, Matchings.java, Point.java, UserListener.java, and MatchingsApplet.html.