Listed on this page are current research projects being offered for the Vacation Scholarship Program.
For more information on this research group see: Discrete Mathematics
Lattice models of polymer systems
Long chain polymers like DNA can be modelled by walks, polygons, trees, and various other combinatorial structures embedded in lattices. This project aims to investigate new polymer models. This can be approached using exact solution techniques or computational methods like series enumeration and random sampling.
Contact: Nick Beaton nrbeaton@unimelb.edu.au
Counting pattern-avoiding permutations and other combinatorial objects
A pattern-avoiding permutation is a permutation whose entries are restricted to avoid one or more substructure. They have simple descriptions but the problem of counting them can range from trivially easy to devilishly difficult. They are connected to a range of other combinatorial objects like lattice paths, binary trees, and inversion sequences. This project will look at some open problems in pattern-avoiding permutations and related objects. Some experience with Mathematica and/or Python would be helpful.
Contact: Nick Beaton nrbeaton@unimelb.edu.au