This page lists some collections of problems possibly of interest to summer research students in Algebra and Combinatorics, together with relevant links.

The main document problems.pdf is a list compiled for this year's Summer Research students. It contains problems about graphs and groups, number theory, and combinatorics, and ends with a mixed bag of miscellanea. Please take a copy and see if there is something there that interests you.

A further document model.pdf describes some problems on the borders of combinatorics, group theory and logic (this is not complete yet!)The document hc.pdf contains a specific question about acyclic orientations of graphs, the "Hanging Curtains conjecture".

I have put a copy of the paper from 2 years ago on the power graphs of torsion-free groups here.

Further contributions (and solutions) welcome!

Please contact me if you want further information about the background to these problems.

Here for the record are the lists of problems that were made available last year. Some progress has been made on some of these.

- Graphs and groups
- Problem list
- Graphs and groups (from 2015)
- Papers on the power graph: arXiv 1705.01586, 1603.04337

- Number theory
- Problem list
- Further details on some of the problems
- arXiv 1111.3507, on 3-factor AP decompositions of the group of units

- Designs from the Sylvester graph
- Factorising the cycle index
- Hot and cold matrices (slides of a talk at LSBU)

Peter J. Cameron

4 June 2018