Two publications

I don’t think it happened to me before that two of my papers were “published” on the same day. Fortunately, it didn’t happen on April Fools’ Day …

One is my paper with Pablo Spiga on switching classes. I described our result last year: the title, Most switching classes with primitive automorphism groups contain graphs with trivial groups, tells you almost everything, except precisely what “most” means: this is “the switching classes of the complete and null graphs and finitely many more”, and we find all the finitely many exceptions. The paper is dedicated to Ákos Seress, and indeed we make a very small improvement to the result of Ákos which inspired our work. I showed, with Peter Neumann and Jan Saxl, that all primitive groups, apart from the symmetric and alternating groups and finitely many others, have a regular orbit on the power set of the domain; Ákos found the finitely many others; Pablo and I add the extra condition that the sets in the orbit should not have cardinality exactly half of the domain (one further group arises). The paper is here, in the Australasian Journal of Combinatorics, my favourite diamond open-access journal.

The other is a paper with Cheryl Praeger, which has been “in preparation” for longer than either of us would like to admit, and which we finished off in Auckland last year to submit to the special issue of the Journal of Algebraic Combinatorics for Chris Godsil’s birthday conference. The paper is here, but you need a subscription to read more than the abstract, I’m afraid. We give a close analysis of symmetric 2-designs admitting a flag-transitive but point-imprimitive automorphism group, including our “new” example of a 2-(1408,336,80) design with automorphism group 212:(3M22:2).

Incidentally, the picture in the Auckland link shows the two co-authors of mine with whom I have most joint papers (9 each).

[On second thoughts, I have had more than one paper in the same issue of a journal in the past; I am discounting that.]

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About Peter Cameron

I count all the things that need to be counted.
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