Rui Viana - REACH Fall 2002

Rui Viana - REACH 2002

| Main Page | Weekly Reports | Math Links | Contact Info |

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.