Combinatorics and Algebra

Combinatorics image showing waterways on a drawing of a town

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.