Category Archives: open problems

unsolved mathematical problems

An exercise in number theory

Posted on 17/02/2023 by Peter Cameron

Here is a cute little problem which I can’t solve. I thought I needed the answer but it turned out that I didn’t, so as far as I know there is no application. Let n = p1a1…psas, where the pi are distinct … Continue reading →

Posted in doing mathematics, open problems | Tagged , | 6 Comments

Two things that should be related

Posted on 03/01/2023 by Peter Cameron

Here are two things that look as if there should be a relation between them. A graph duality In my paper on graphs defined on groups, I invented an ad hoc duality relation between pairs of graphs. The context is … Continue reading →

Posted in exposition, open problems | Tagged , , , | 4 Comments

BCC29 at Lancaster

Posted on 20/07/2022 by Peter Cameron

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 →

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I’d like to see this solved

Posted on 17/06/2022 by Peter Cameron

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

Posted on 01/06/2022 by Peter Cameron

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 →

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Graphs on groups, 9

Posted on 08/11/2021 by Peter Cameron

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 →

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Clive Sinclair

Posted on 18/09/2021 by Peter Cameron

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 →

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Graphs on groups, 8

Posted on 16/08/2021 by Peter Cameron

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 , , | 3 Comments

A small problem

Posted on 26/07/2021 by Peter Cameron

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 →

Posted in open problems | Tagged , , | 1 Comment

A little problem

Posted on 31/05/2021 by Peter Cameron

In connection with the power graphs of unitary groups, I came across the following little number-theoretic 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 →

Posted in open problems | Tagged , , | 6 Comments