Top Posts
Recent comments
Blogroll
- Alexander Konovalov
- Annoying precision
- Astronomy Picture of the Day
- Azimuth
- Bad science
- Bob Walters
- British Combinatorial Committee
- CIRCA tweets digest
- CoDiMa
- Coffee, love, and matrix algebra
- Collecting reality
- Comfortably numbered
- Computational semigroup theory
- DC's Improbable Science
- Diamond Geezer
- Exploring East London
- From hill to sea
- Gödel's lost letter and P=NP
- Gil Kalai
- Haris Aziz
- Intersections
- Jane's London
- Jon Awbrey
- Kourovka Notebook
- LMS blogs page
- Log24
- London Algebra Colloquium
- London Reconnections
- Marie Cameron's blog
- MathBlogging
- Micromath
- Neill Cameron
- neverendingbooks
- Noncommutative geometry
- numericana hall of fame
- Paul Goldberg
- Ratio bound
- Robert A. Wilson's blog
- Sheila's blog
- Since it is not …
- Spitalfields life
- St Albans midweek lunch
- Stubborn mule
- Sylvy's mathsy blog
- SymOmega
- Tangential thoughts
- Terry Tao
- The Aperiodical
- The De Morgan Journal
- The ICA
- The London column
- The Lumber Room
- The matroid union
- Theorem of the day
- Tim Gowers
- Vynmath
- XKCD
Find me on the web
Cameron Counts: RSS feeds
Meta
Category Archives: open problems
Graphs on groups, 5
I gave two lectures on this stuff to a new research seminar on Groups and Graphs, run by Vijayakumar Ambat in Kochi, Kerala. The first was an introduction to the hierarchy, the second was about cographs and twin reduction, why … Continue reading
Posted in events, exposition, open problems
Tagged cograph, commuting graph, nilpotent group, perfect graph, power graph
2 Comments
Graphs on groups, 4
Here is a small problem, mixing group theory and number theory, which might appeal to someone. A couple of definitions. The power graph of a group G has an edge from x to y if one is a power of … Continue reading
Induced subgraphs of power and commuting graphs
For those who like thinking about these things, here is a small observation and a few problems. As I have recently discussed, the power graph of a group is perfect. This means that all its induced subgraphs are perfect, and … Continue reading
Ramanujan+100
I have just spent the last four days in Kochi, Kerala, at the International Conference on Number Theory and Discrete Mathematics, commemorating Srinivasa Ramanujan, the great Indian mathematician, on the 100th anniversary of his far-too-early death. The conference had perhaps … Continue reading
Oligomorphic groups: topology or geometry?
One perhaps unexpected result of the pandemic is that there is a huge volume of really interesting mathematics flying around the internet at the moment, courtesy of Zoom and other platforms. This week I went to a talk by Joy … Continue reading
Between Fermat and Mersenne
The following problem came up in something I was doing recently. I have no idea how difficult it is – it looks hard to me – but I would be glad to hear from anyone who knows more than I … Continue reading
Association schemes for diagonal groups
Sean Eberhard commented on my posts on diagonal groups (see here and here). He is correct; there is an association scheme preserved by the full diagonal group with n factors in the socle; it is non-trivial if n > 2. The details … Continue reading
Posted in open problems
Tagged association scheme, diagonal group, Latin hypercube, Latin square
1 Comment
Fair games and Artin’s conjecture
A few years ago I described Persi Diaconis’ response to G. H. Hardy’s claim that there is a real dividing line between real and recreational mathematics. (See the report here.) This led from Persi’s first experiments in card shuffling to Artin’s conjecture … Continue reading
Kourovka Notebook, 19th edition
The latest edition (the 19th) of the Kourovka Notebook has just been released. It now has its own website, https://kourovka-notebook.org/. The Kourovka Notebook has been going for more than 50 years, longer than my life as a mathematician. It is … Continue reading
Posted in doing mathematics, history, open problems
Tagged identical relations, Kourovka Notebook, open problems
1 Comment
Polynomially bounded orbit counts
The best news I had yesterday was an email from Justine Falque with a link to a paper that she and Nicolas Thiéry have just put on the arXiv. The 12-page document is only the “short version”, and a longer … Continue reading