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 Peter Cameron on Scottish Combinatorics Conference
 Josh Paik on Scottish Combinatorics Conference
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Author Archives: Peter Cameron
London Combinatorics Colloquia 2023
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
John Bullough
I never met John Bullough, and had never heard of him until his death was reported a few days ago. But I owe him a great debt. He founded the Scottish Charity Air Ambulance. After Rosemary fell into the Kenly … Continue reading
Bases
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
Posted in doing mathematics, exposition
Tagged bases, irredundant bases, minimal bases, Mornington Crescent, permutation groups
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Orthogonal block structures
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
Posted in doing mathematics, exposition
Tagged association scheme, partition lattice, permutation group, statistics
1 Comment
George F. Simmons
Browsing a back issue of the BSHM bulletin, I found a review of the book Calculus Gems by George F. Simmons, from which I learned that he died in 2019 at the age of 94. I never met Simmons, and … Continue reading
New web address
Thanks to all of you who made suggestions about moving my webpages, since the University will take the old ones down at the end of the month. GitHub was the most popular suggestion, so I went with that. The new … Continue reading
Birthday conferences
The impending removal of my university web pages has led me to put here the slides of some talks. I have been extremely fortunate in having wonderful colleagues who have organised three birthday conferences for me. (Well, one was actually … Continue reading
Posted in doing mathematics, events
Tagged graphs, homogeneous structures, permutation groups, primitivity, semigroups, synchronization
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Between transitive and primitive
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 2transitivity. Here is a new … Continue reading
Posted in doing mathematics, exposition
Tagged permutation groups, primitive, quasiprimitive, transitive
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An exercise in number theory
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 Euler's function, multinomial coefficient
6 Comments