James is a second year student studying a Bachelor of Mathematics(Majoring in Applied and Computational Mathematics, with minors in Discrete Mathematics and Simulation Science) at QUT. He is interested in Discrete Mathematics as well as modeling and simulation in Computational Mathematics. His AMSI Project will be in combinatorics.
Skolem Sequences And Graphs
Skolem sequences are a combinatorial structure, which can be used to construct a variety of other structure such as Steiner triple systems. Skolem circles are a generalisation of Skolem sequences. Some (but not all) Skolem circles can be represented as the Skolem labelling of a graph. This project will explore the conditions under which valid Skolem sequences and circles form. This will be achieved by enumerating the number of distinct skolem circles for the first few orders and formulate a general lower bound on the number of distinct Skolem circles.