Category Archives: doing mathematics

how is it done?

Graphs on groups, 12

Posted on 03/01/2022 by Peter Cameron

One thing I have learned from the project is that the most interesting question about graphs defined on groups is this: given two types of graph defined on a group G, what is the class of groups for which the … Continue reading →

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Graphs on groups, 11

Posted on 02/01/2022 by Peter Cameron

A brief interlude to describe another recent preprint, and as in the preceding post I will concentrate on one result in the paper. I don’t know why it happens, but in this project one of the most interesting graph parameters … Continue reading →

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Graphs on groups, 10

Posted on 01/01/2022 by Peter Cameron

The lesson of this post and the next in the series is that the most interesting questions (to me, anyway) are not about the girth of the deep commuting graph but instead about the classes of groups G defined by … 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 →

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A new constant?

Posted on 23/05/2021 by Peter Cameron

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 →

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Graphs on groups, 2

Posted on 27/01/2021 by Peter Cameron

I wrote the long post about this to try to write it out of my system. No luck … I mentioned in that survey that every finite graph is embeddable as induced subgraph in the enhanced power graph, deep commuting … Continue reading →

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Ramanujan+100

Posted on 15/12/2020 by Peter Cameron

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 →

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Oligomorphic groups: topology or geometry?

Posted on 10/12/2020 by Peter Cameron

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 →

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