So there are no examples of rank at most 4; we know just two of rank 5; and infinitely many of rank 6.

]]>Gordon: I have challenged James Mitchell to compute the endomorphism monoid of this graph. It might be interesting to see just what else is there. ]]>

Probably not of much significance, but your graph has other non-uniform endomorphisms too – for example, one with fibres of size 5,5,5,5,5,10,10 whose image is three triangles arranged in a path. (Presumably this is just a refinement of the one you’ve exhibited, but I haven’t checked that.)

]]>It is a curious situation anyway. The LMS journals have been produced by a variety of publishers: for my first paper it was a small East End firm called Hodgsons, if I remember correctly; later it was Cambridge University Press, now it is Oxford. Oxford have custody of all the archived material, whether they first published it or not. Given this, you might have thought they could be a little generous about allowing access to it; but apparently not.

I assume it is OUP rather than the LMS driving this, since it seems that back issues of the Quarterly Journal are also not freely available.

I haven’t had a chance to ask Susan Hezlet yet, but will do so sometime.

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