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24-28/06/2003
Bled, 21-28 June 2003 (part II)
Peter Cameron2006-03-12 12:14:02
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24/06/2003
The aches plagued me all night and kept me awake; it was very hard to get comfortable. A hot shower helped a bit.
The morning was sunny, the faces of the distant mountains bright white - no wonder they take the colours of sunset so beautifully. I couldn't settle to anything before my talk, but once the adrenaline got flowing I was fine. Someone in the audience suggested delta-matroids as the right concept for permutation group bases: I don't think so but I will check.
Bojan Mohar made an interesting suggestion. As well as minimal base size, he has considered the smallest cardinality of a set of points with the property that the meet of the orbit partitions of their stabilisers is trivial. Of course such a set is a base, so this number is not smaller than the minimal base size. He has examples (automorphism groups of Paley graphs of prime order) where the base size is 2 but his invariant is about log n.
During the morning talks I remembered that I have seen something like this before! Laci Babai bounded the order of a uniprimitive permutation group by bounding the base size, and if I am not mistaken he did this by bounding the "separation number" in Bojan's sense.
Also, the definitions of irredundant, minimal and (probably) greedy base extend to separating sets in this sense. Lots of interesting stuff to work on here!
I walked round the lake, stopping for a pizza at the beach near the outflow (and of course it was far too much). The breeze had got up; waterlilies and swans bounced up and down on the chop.
In the late afternoon, a cracker storm blew up. The power flickered, and the computers in the conference office lost their internet connections. From the back of the lecture room, the rain sounded really heavy. But by dinnertime, it had stopped, and the sun shone from under the cloud cover.
Dinner was traditional Slovenian food, by candlelight
...
See photographs from:
Slovenia Gallery
