FURI | Spring 2018

Enumeration of Self-Avoiding Walks in Self-Organizing Particle Systems

The objective of this research will be to investigate different approaches for counting and bounding the number of closed, self-avoiding walks with a given length, which are unique up to the translation on the triangular lattice. If new bounds are proven, the new values will be used to inform tighter bounds on the bias parameter for a compression algorithm implemented in a self-organizing particle system. Counting such walks is equivalent to counting the number of unique particle configurations, with the given perimeter, within such a system.