Combinatorics and Algebra

The interests of the Combinatorics and Algebra research group include the following topics.

• Graph theory: graph parameters; well-quasi-ordering; extremal graph theory; decompositions; position problems
• Combinatorial designs: automorphisms and embeddings; infinite designs; homogeneous Steiner triple systems and their links with model theory
• Discrete geometry
• Latin squares and quasigroups
• Pattern-avoiding permutations and their connection with graph theory
• Theory of symmetric maps on surfaces
• Optimal network design; degree-diameter problem and cages
• Automorphism groups of combinatorial objects
• Extremal and probabilistic combinatorics
• Homogeneous relational structures and Cherlin's notion of the "relational complexity" of a finite permutation group
• Generating groups using geometries

The Group organises a regular series of online seminars in discrete mathematics and holds the one-day OU Winter Combinatorics Meeting in January every few years.