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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.

Combinatorics and Algebra Group