Enumerative Combinatorics
Research Groups
- Actuarial and Financial Mathematics
- Applied Algebra and Information Theory
- Bayesian Statistics
- Computational Mathematics and High-Performance Computing
- Enumerative Combinatorics
- Functional Analysis
- Mathematics Education
- Matrix Analysis
- Number Theory
- Potential Theory
- Probability
- Quantum Information and Computation
- Real Algebra
- Relativity and Mathematical Physics
- Statistical Genetics and Bioinformatics
- Statistical Modelling
- Waves, Fluids and Turbulence
Enumerative Combinatorics
Enumerative combinatorics, while primarily motivated by counting problems, concerns the study of structures and their representations that have proven useful in an enumerative context. Our interests lie in several of the main topics in enumerative combinatorics, such as permutations and their representations, partially ordered sets, theory of partitions, Young tableaux, symmetric functions and q-analogues in combinatorics, such as q-(poly)matroids, subspace designs, and invariants of codes. Another source of motivation for our work is the combinatorics that arises in number theory, coding theory and statistical physics.
People
Assoc Prof Eimear Byrne
Research Interests: Algebraic coding theory, codes over rings, codes and graphs, network coding, finite rings & fields, Groebner bases, decoding algorithms, APN functions, algebra in communications
Assoc Prof Mark Dukes
Research Interests: Algebraic & enumerative combinatorics, discrete mathematics, and their use in the analysis of complex systems.
Assoc Prof Robert Osburn
Research Interests: Number Theory, Q-Series, Modular Forms.
PhD students
Kevin Allen
Research interests: Combinatorics, knot theory, number theory.
Amal Alofi
Research Interests: Sandpile models on bipartite graphs.
Giuseppe Cotardo
Research Interests: Rank metric codes, tensor codes, bilinear complexity, geometric lattices.