Author Archives: Peter Cameron

About Peter Cameron

I count all the things that need to be counted.

Pseudofields, quasifields, near-domains

Here is a piece of evidence which those who think that mathematics is invented rather than discovered will like. This concerns definitions. I wrote last year about the definitions of a group, a matroid, the real numbers, and primitivity. In … Continue reading

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Counting coauthors, 2

I have decided to move one step towards practising what I preach. The arXiv is now the de facto place of publication of many mathematics papers; Google Scholar recognises it, as do various other sites such as ResearchGate. So shouldn’t … Continue reading

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Evoa

A very different kind of excursion last Sunday, to Evoa, a nature reserve near the Tejo estuary. Quite a drive from Lisboa: along the highway to Vila Franca, and the iron bridge which was the last bridge across the Tejo … Continue reading

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Tomar

The Portuguese city of Tomar was founded, on the site of a Roman town, by the Knights Templar in the twelfth century. (Many businesses in the town still use the Templar name or their logo, which is also found in … Continue reading

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Comics, literacy and self-help

Neill recently spent a week pouring out his passion and commitment to children’s comics on his blog. I thought it made remarkable reading. It is indexed on a side panel, or you can get the series from Readlists (a site … Continue reading

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9,21,27,45,81,153,…

This is the sequence of degrees of primitive groups which don’t synchronize a map of rank 3, equivalently graphs with clique number and chromatic number 3 having primitive automorphism groups. You could argue that the sequence should start with 3, … Continue reading

Posted in doing mathematics, open problems | Tagged , , , , , | 2 Comments

Butterflies

I am in Lisbon working with João Araújo and Wolfram Bentz on synchronization. We say that a permutation group G on the set {1,…n} synchronizes a non-permutation f from this set to itself if the semigroup generated by G and … Continue reading

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