Combinatorics is one of the underpinnings of theoretical computer science.
Our current research
Our research interests are in enumerative, bijective and algebraic combinatorics. The research spans a wide spectrum, with recent emphasis on permutation patterns, combinatorics on words, graph theory and applications to physics and biology.
This is a relatively young, but very active, research area. The driving force behind much of our work is to find connections between families of different combinatorial structures.
We've also recently been working with lattice paths, plane trees, planar maps and Ferrers diagrams with various types of fillings. The goal is to find connections between different kinds of combinatorial objects, in the form of bijections that send a set of statistics on one side to a set of statistics on the other. Such statistics-preserving bijections not only reveal structural similarities between different combinatorial objects, they often also reveal previously unknown properties of the structures being studied.
Combinatorics on words
This is a relatively new research area in discrete mathematics. The motivation comes not only from different modern, as well as classical, fields of mathematics, but also from computer science, physics, and biology. Many fundamental results of the theory have been discovered, or rediscovered, when using words as tools for other sciences.
We're also further developing our work in algebraic combinatorics, with an emphasis on algebraic and topological properties of simplicial complexes.
The Strathclyde Combinatorics Group is led by Professor Einar Steingrimsson. The rest of the team includes: