Category Archives: exposition

a post aimed to teach something

Regular polytopes, 1

One of the topics I am thinking about with Dimitri Leemans at present concerns regular polytopes. He and his co-authors Maria Elisa Fernandes and Mark Mixer have produced some nice results and a tantalising problem about these objects. I will … Continue reading

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A symmetric design

Quite a long time ago, Arunas Rudvalis discovered a symmetric 2-(14080,1444,148) design: a set of 14080 points, with 14080 subsets of size 1444 called blocks, with the property that any point lies in 1444 blocks, any two points in 148 … Continue reading

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A cliff

The “combinatorial explosion” is a well-known phenomenon. I recently came across a very dramatic example of it. I was trying to compute the function F(n,k), defined to be the maximum of |S|×|P|, over all sets S of k-subsets and all … Continue reading

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Groups, lattices and bases

About ten years ago I wrote a six-page paper, which I didn’t succeed in getting any journal editor to publish. I will say a bit about its contents below, but you can read it now: I have posted it on … Continue reading

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Easy to state, hard to solve?

I described here how Pablo Spiga and I showed that all but finitely many nontrivial switching classes of graphs with primitive automorphism group contain a graph with trivial automorphism group, and found the six exceptions. (The trivial switching classes are … Continue reading

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Primitive switching classes

Last year I wrote here about switching classes of graphs for which the switching class has a primitive automorphism group. (I repeat the definitions briefly below.) I conjectured that, except for the trivial switching classes of the complete and null … Continue reading

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Automorphism groups of hypergraphs

I am getting old and forgetful, but I don’t think I said anything here about this problem yet. If I did, apologies for the repetition – but there is something new to report! In April, Laci Babai and I finally … Continue reading

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