Donald Preece memorial day

Donald Preece

Donald Preece Memorial Day

On Thursday, 17 September, in the Fogg Lecture Theatre at Queen Mary University of London, there will be a memorial day for Donald Preece, statistician, combinatorialist, and organist.

Put the date in your diary, and bookmark the web page, where further details will be announced later.

Some links about Donald Preece:

R. A. Bailey, P. J. Cameron, L. H. Soicher

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Eclipse non-event

Today there was a solar eclipse, they say.

We were told that the sun would be 85% covered in London at 9.30am. But the clouds were so thick that nothing was visible, not even a dimming of the light. So we went home and watched the streamed video from Longyearbyen in Svalbard.

I think the last solar eclipse in London was in January 2011, when the sun rose partially eclipsed. We got up early and walked down to the Thames path to watch it over the river. But, as I reported here, clouds hid the sun, although an eerie quality of light was noticeable.

I do count myself very lucky in having had a good view of a total eclipse. In 1999, we were in Paris at the time. Plotting the line of totality on a French railway map, we decided that Grandvilliers would be a good place to go to see it. We took an early train from Gare du Nord and walked out into the countryside until we found a comfortable spot. This was possibly the only place in western Europe that was cloud-free; we were able to watch the entire thing without interruption. An experience to which the over-used word “awesome” really applied!

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Folding de Bruijn graphs

I wrote recently about foldings of de Bruijn graphs, why we are interested in them, and how pleased I was that we had agreed that the de Bruijn graph with word length 4 over a 2-letter alphabet has 1247 foldings (or said otherwise, there are 1247 automata over a 2-letter alphabet whose state is determined by the last four symbols read).

Well, now we have a formula for the number of foldings of de Bruijn graphs with word length 2 over arbitrary alphabets, which (programmed in GAP) can compute the number for alphab et size 20 in 700 milliseconds, and alphabet size 30 in 50 seconds.

I won’t describe the formula here. The computation involves nested loops, the outer loop over partitions of the alphabet, and the inner loop over partitions of the set of parts in the outer loop; the inner loop implements a Möbius inversion over the lattice of set partitions, while the outer loop sums products of the function computed by the inner loop.

I am discussing it here because of a sidelight on how mathematics gets done. I was trying to understand the fact that, for word length 2 over alphabet of size 3, there are 192 foldings. I had observed that 192 = 53+3×22+1; I knew where the first and last terms came from but was thinking about 22. I went to bed, and as I lay there going to sleep I understood how to get this number (it is B(2)(B(4)−B(2)2), where B(n) is the nth Bell number). So I went to sleep, confident that I could reproduce the argument in the morning.

Well, of course, the next morning, I tried to write it out and got stuck, and by the evening I hadn’t got unstuck. So I went back to bed, and replayed my mental processes, and back it came in full clarity. I didn’t leap up and write it down, but simply rehearsed the argument until it was absolutely clear to me and I was sure I could recover it in the morning.

And, sure enough, I could!

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Farewell Terry Pratchett

There is no point in trying to add to what others have said so well. Go look at XKCD,

or London Reconnections,

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Representing the Fano matroid

In my lecture today I proved that the Fano matroid is representable over a field F if and only the characteristic of F is 2. There is a proof of this using only the classical theorems of Ceva and Menelaus from Euclidean geometry. (This was not quite the proof I gave, since nobody knows these theorems now!) But I thought I would record it here.

Here is the Fano plane. As a matroid, the independent sets are all sets of at most two points, and the sets of three points which are not lines of the plane.

Fano plane

Consider the figure without the “curved” line. This is the diagram for Ceva’s theorem. It shows that, if we take x, y and z to be inhomogeneous coordinates of the points 6, 3 and 5 on the lines of the outer triangle, then xyz = +1, by Ceva’s Theorem.

Now consider the figure with only the outer lines of the triangle and the “curved” line, which is then a transversal to the three sides; so xyz = −1, by Menelaus’ Theorem.

So we must have +1 = −1, so that the characteristic is 2.

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Lost worlds

I am in St Andrews, and most of my books are in London, so I tend to pick up books I have read before.

One of my all-time favourites is Michael Bywater’s Lost Worlds, subtitled What have we lost, and where did it go? This extraordinary book (a collection of essays on topics including Bayko, Fug, God, Noddy, and Sandwich, Ham, the Railway) is by turns witty, poignant, learned, and baffling. I can’t just quote bits from it to give you the flavour, since I would end by transcribing the whole thing; so instead here is the second index entry under each letter (except X, where there is only one entry, Xanadu).

  • aardvark, deployment of for competitive advantage
  • baby clothes, giant
  • Cairo, the Geniza of
  • Daily Mail: desire to be editor of; making readers feel fat; measured views on asylum-seekers; mistaken lynchings by readers of; not a known cause of cancer; snobbery of its readers
  • Earth, the End of the, commemorated in snuff
  • facial hair, the musical influence of
  • gadgets, author’s embarrassing collection of
  • hair, men’s: consequences of running your hands through; lost guide to the care of
  • idiots, the contemptibility of
  • Jantzens
  • Kayser Bondor
  • Lady Chatterley trial
  • mackerel, new, melodious
  • The Name of the Rose, possibly a mistranscription
  • oblivion: certainty its inevitable precursor; paradox of; personal, inevitable, celebrity a struggle against
  • paedophilia, unwarranted cries of
  • Queer Eye for the Straight Guy, serious competition for, ecclesiastical
  • racks, multiple, fretwork, essential in 1930s home
  • saddened, Microsoft feeling
  • Tanner, Dr Michael, the sensory persistence of, see also Rhinoceros
  • uncle, satisfying nephew’s wife, on lavatory door
  • values, Victorian, unsurprising
  • waiters, Chinese, deracinated
  • yearnings, paradoxical, songs of, Portuguese
  • zlotys, soggy, rumpled

(Actually I cheated on a couple of those.) Give yourself a point if you can make a good guess about what they refer to!

You will not be surprised to learn that the author was a friend of Douglas Adams, and even claims to be the inspiration for Dirk Gently. The last item in the book, “Zone, the Dead”, contains a poignant story about Adams, not named in the text but identified in the index.

A final note: in describing the final prayer of Compline, Bywater remarks that perfect “loses the soft and telling resonance of the Latin: that perfectus itself comes from the verb perficere: to carry out, to finish or complete.”

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British Combinatorial Committee

Announcing a new website for the British Combinatorial Committee:

The British Combinatorial Committee is a charity, registered in Scotland, whose objective is the support of combinatorial and discrete mathematics in the United Kingdom. I have the honour of being the chair of the Committee. The fact that it is registered in Scotland is really a historical accident: over the period when we made this change, several key officers of the committee, including John Sheehan, Ian Anderson, Peter Rowlinson, and Keith Edwards, were based in Scotland. (What we would have done if the Scottish independence referendum had produced a different result is not clear, though I hope it would not have made much difference.)

The Committee oversees various activities, chiefly the biennial British Combinatorial Conference (the next one is at the University of Warwick – see you there!). We also support various conference sequences and one-offs in Britain, publish an annual Bulletin and more frequent Newsletters, and so on, in accordance with our constitution (which you can find on the new website). One of our features is a list of conferences in combinatorics and related areas (which I have interpreted fairly widely since I have been running it).

Since I retired from Queen Mary in 2012, maintaining a website there has been a bit of a stretch, and I felt a bit vulnerable to accidents such as forgetting to update my password and losing access. Better, I thought, to have the website somewhere that is not dependent on university administrators or IT staff, and which can easily be taken over when it becomes necessary.

So I got around to moving much of the material at Queen Mary to the new website, and updating it at the same time. (This is one of several jobs where I got a bit behindhand: my apologies if you sent me details of a conference and I was seriously slow in responding. Hopefully normal service has now been resumed.)

Anyway, take a look at the new website. A WordPress site distinguishes between posts (which are topical and assumed to be of only short-term interest) and pages (which are static, though of course they can be updated). Most of our information will be on pages, but I intend to use posts to highlight upcoming conferences or news items, and perhaps for conference reports, book reviews, and so forth, if I can persuade people to write them. My co-conspirators are Keith Edwards, James Hirschfeld, and David Penman.

Let me know what you think; and most important, send me information which should appear on the site (either by email, or by commenting on what is there).

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