Category Archives: exposition

a post aimed to teach something

Steiner systems exist, 2

One of the inevitable consequences of getting old is that my brain becomes more and more like a Swiss cheese, and important pieces of information fall through the holes. So I owe an apology to Michael Braun, Tuvi Etzion, Patric … Continue reading

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Real v recreational mathematics

A footnote to my report on Persi Diaconis’ lecture on Martin Gardner. Persi challenged us to consider the question: Is there a sharp division between “real” mathematics and “recreational” mathematics, and if so, where does it come? G. H. Hardy clearly thought … Continue reading

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Generation, t-designs and other mathematical notation

Donald Knuth, a mathematician (his adviser was Marshall Hall, his thesis on algebraic structures related to projective planes) turned computer scientist, became dissatisfied with typesetting while producing his multi-volume The Art of Computer Programming. So he took time off to … Continue reading

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Entropy and groups

Yesterday I gave a talk on a theorem of Terence Chan, which he spoke about at a network coding meeting at Queen Mary in late 2012. He sketched a proof on the common room table after the talk, and I … Continue reading

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Poly-Bernoulli numbers

With Celia Glass and Robert Schumacher, I recently found a combinatorial interpretation of the poly-Bernoulli numbers of negative order. Bernoulli numbers The classical Bernoulli numbers are defined by a recurrence which can be written symbolically as (B+1)n+1 = Bn+1. The interpretation is: … Continue reading

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From the archive, 5

The first of my two papers with Paul Erdős was published in 1990 in a conference proceedings, and is a bit inaccessible; I have never managed to find a copy on the web. The Hungarians are collecting electronic copies of … Continue reading

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Primitive lambda-roots

Nearly ten years ago, Donald Preece and I wrote the first draft of a set of notes on primitive lambda-roots. We could never decide what do do with them: they were too short for a monograph, too long (and expository) … Continue reading

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From the archive, 4

A photocopy of a sheet of paper in my handwriting. At the top left, my initials are written in the handwriting of Jaap Seidel. The page begins as follows. Theorem. Let X be a set of points in the n-cube … Continue reading

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Eigen-species

The title of this post is half-serious: it is designed to catch attention, but I think there are interesting things lurking here which deserve more exploration. Species A species describes a class of objects built on finite sets, in a … Continue reading

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From the archive, 2

Next up is a document which is just over a quarter-century old, a photocopy of a 26-page handwritten document entitled “On doing geometry in CAYLEY”. The background, as explained in the document, is that John Cannon’s computer algebra system CAYLEY, … Continue reading

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