Category Archives: exposition

a post aimed to teach something

London Combinatorics Colloquia 2023

Posted on 17/05/2023 by Peter Cameron

In London last week for this (usually) annual event, now happily back live. In contrast to usual practice, I will discuss the second day first. Norman Biggs was the founder of the combinatorics group at the London School of Economics, … Continue reading →

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Bases

Posted on 15/04/2023 by Peter Cameron

A base for a permutation group is a sequence (a1,…,ar) of points in the permutation domain whose pointwise stabiliser is the identity. Bases were introduced in computational group theory by Charles Sims, since two elements of a permutation group are … Continue reading →

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Orthogonal block structures

Posted on 09/04/2023 by Peter Cameron

If you google “commuting equivalence relations” you will find signs of a large and rich literature. I want to talk about one aspect, on the border of algebraic combinatorics and experimental design: orthogonal block structures. Look up orthogonal block structures … Continue reading →

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Between transitive and primitive

Posted on 09/03/2023 by Peter Cameron

Many familiar properties of permutation groups form a hierarchy. A few years ago, with João Araújo and Ben Steinberg, I wrote a survey on properties related to synchronization of finite automota, lying between primitivity and 2-transitivity. Here is a new … Continue reading →

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Mathematical Structures

Posted on 13/01/2023 by Peter Cameron

My last major job at Queen Mary University of London more than ten years ago was designing and presenting a new first-semester first-year module to be taken by all students on mathematics programmes or joint programmes involving mathematics. I discussed … Continue reading →

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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 →

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A theorem on polytopes

Posted on 27/12/2022 by Peter Cameron

You know what polygons and polyhedra are. How do we extend their study to higher dimensions? There are two parts to this question. The first involves incidence geometry: vertices, edges, faces, etc. Here the generalisation is fairly straightforward. A polygon … Continue reading →

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The road closure property

Posted on 21/12/2022 by Peter Cameron

My work with João Araújo and other semigroup theorists has produced a number of permutation group properties which lie between primitivity and 2-homogeneity, especially the synchronization family. Another of these is the road closure propery, which I have discussed here … Continue reading →

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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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Peter Neumann’s 3p paper

Posted on 15/04/2022 by Peter Cameron

In 1955, Helmut Wielandt published a paper proving the following theorem: Let G be a primitive permutation group of degree 2p, where p is a prime greater than 3, which is not doubly transitive. Then p = 2a2+2a+1 for some positive integer … Continue reading →

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