Category Archives: Combinatorics

Coincidences among small groups

I like to study reflection groups of various kinds.  Let Sn denote the group of permutations of n points, let GL(n, q) denote the general linear group of invertible linear transformations of an n-dimensional vector space over the finite field with … Continue reading

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As I mentioned, after Vancouver I went to a conference at Herstmonceux Castle in Sussex, England.  It was mathematically excellent, and I feel that BBC detective shows properly prepared me for my first visit to the UK.  Trees in England … Continue reading

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The Erdős FBI file

A cute little article here about Paul Erdős’s FBI file.  The short version is … that it’s not very interesting; the FBI routinely (and correctly) determined that he was just interested in doing mathematics.  In a Minnesota-centric note, it was … Continue reading

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Proof by induction

If you’re solving a combinatorial problem depending on a parameter n and the first few values are 1, 1, 2, 5, 14, your sequence is the Catalan numbers.  If the next term of the sequence is 42, that constitutes a … Continue reading

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“My brain is open” by Bruce Schechter

My Brain Is Open is one of two biographies of Paul Erdős that I know of, the other being Hoffman’s The Man Who Loved Only Numbers. I mostly enjoyed this one; it conveyed a good sense of the subject’s eccentricities … Continue reading

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Ken Appel has died

The Times has a very nice obituary of Kenneth Appel, the main mastermind behind the proof of the four-color theorem, one of the crowning achievements of graph theory. He also sounds likfair pleasant, interesting man. The advent of computers has … Continue reading

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Generating series

Last Wednesday morning lecture, to calculus students, in two sentences: A series that looks like is called a Taylor series.  We are very interested in understanding these series and the functions they represent, so it is of the utmost importance … Continue reading

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