Avoiding Differences

As one part of my PhD research, I investigated the Triangle Conjecture of Dominique Perrin and Marcel-Paul Schützenberger. Although disproved shortly after its inception by Peter Shor, I soon realized that the real key behind the conjecture was the quantity

f_Δ(n) = the size of the largest subset of [n] avoiding differences in Δ,

where one avoids differences in Δ by making sure that no two elements of the set have a difference in Δ. Numerous results were discovered and proved by me, and it all started through investigations in Mathematica and Java code. This website is the home for this code, which will continually be updated. It is protected under the GNU General Public License; details to be provided soon.

Mathematica

Click here for the Mathematica code.

Java

Click here for the Java code. It is a .zip file that contains seven .java files, all in the package com.myraff.avoid.

Future Work

There are plenty of things left to do in this project.