Unavoidable Sets
Abstract   Implementation   Paper (PDF)  


Francine Blanchet-Sadri, Sean Simmons and Eric Weissenstein

The applet below provides an implementation in Java. This page may not function correctly if you do not have Java 1.6 or higher from Sun Microsystems.

The program below provides a means of investigating the properties of the set Y m|n1,n2 , where Y m|n1,n2 ={a^ m a,b^ m b,a^n1a^n2a,b^ n1b^n2b}, given that ^ represents a hole.

The user inputs values for m,n1,n2 (note that though the program takes large integers, once the integers get large the program is likely to take a long time or even crash, and the graphics will not be as good). The program then determines whether the given set Ym|n1,n2 is avoidable or unavoidable. Once this has been determined, it relays this information to the user, and outputs a graphic representation of the graph Hm|n1,n2. More, if the set is avoidable then the program colors the graph in such a way that it avoids Y m|n1,n2 , using the colors red and blue to represent a and b (or vice versa).