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Category Archives: open problems
BCC29 at Lancaster
Last week we celebrated the 29th British Combinatorial Conference in Lancaster, face to face. (As a side observation, this was by far the largest social gathering I have been at since the start of the pandemic; I found it both … Continue reading
I’d like to see this solved
Here is a problem that I would really like to see solved. I have spent quite a bit of time on it myself, and have suggested it to a few other people, but it still resists all attacks, though it … Continue reading
Posted in doing mathematics, open problems
9 Comments
A problelm
Given a finite permutation group G on a set X, the permutation character π of G is the function on G mapping an element g to its number of fixed points in X. This is a character of G, the … Continue reading
Graphs on groups, 9
We continue to make progress with the graphs on groups project, but this post attempts to step back and look at the whole thing. What use is all this? Once, after I talked at a departmental colloquium at the University … Continue reading
Posted in doing mathematics, exposition, open problems
Tagged graph theory, group theory, number theory, open problems
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Clive Sinclair
Yesterday I read the news that Clive Sinclair has died. This brought back memories of my first encounter with personal computers nearly 40 years ago. At the time I had a demanding job and three small children, and I was … Continue reading
Posted in doing mathematics, history, open problems
Tagged Neil Calkin, sumfree sets, ZX Spectrum
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Graphs on groups, 8
The dark clouds seem to have lifted a bit. Perhaps now, that the last rush of conferences for a while is over, life can return to something like normality … For me the most significant event was the last in … Continue reading
Posted in doing mathematics, events, open problems
Tagged graphs and groups, matching number, power graph
3 Comments
A small problem
In connection with the research discussion about graphs and groups, I began to wonder which finite groups have the property that any two elements of the same order are conjugate. I thought about this, and got a certain distance, and … Continue reading
A little problem
In connection with the power graphs of unitary groups, I came across the following little numbertheoretic conundrum. Can anyone solve it? Let q be an odd power of 2 (bigger than 2). Show that (q2−q+1)/3 is not a prime power … Continue reading
A new constant?
This is an appeal for help. Has anyone come across the constant 2.648102…? Here is the background, which connects with my previous posts about graphs on groups. We are interested in the clique number of the power graph of the … Continue reading
Posted in doing mathematics, open problems
Tagged clique number, Euler's function, power graph
8 Comments
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