Category Archives: exposition

a post aimed to teach something

London Combinatorics Colloquia 2019

Posted on 11/05/2019 by

In London last week for the two combinatorics colloquia, at Queen Mary and LSE. The weather was unusually grey and rainy; it seems in retrospect that it is almost always fine and sunny for this event, but I know that … Continue reading →

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Fair games and Artin’s conjecture

Posted on 10/04/2019 by

A few years ago I described Persi Diaconis’ response to G. H. Hardy’s claim that there is a real dividing line between real and recreational mathematics. (See the report here.) This led from Persi’s first experiments in card shuffling to Artin’s conjecture … Continue reading →

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A family of non-synchronizing groups

Posted on 06/01/2019 by

As I explained recently, according to the O’Nan–Scott Theorem, a finite primitive permutation group either preserves a Cartesian structure, or is of affine, diagonal or almost simple type. In all these types except the last, the action of the group … Continue reading →

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The Hall–Paige conjecture

Posted on 18/12/2018 by

A Latin square of ordern is an n×n array of symbols from an alphabet of size n with the property that each symbol in the alphabet occurs once in each row or column. Two Latin squares L and M are … Continue reading →

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Normal

Posted on 14/11/2018 by

There are various overused terms in mathematics. “Normal” is one of them. Perhaps the four commonest uses are the following: A complex square matrix is normal if it commutes with its conjugate transpose. Normal matrices are precisely the ones which … Continue reading →

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Synchronization update

Posted on 30/10/2018 by

There is some recent news about the synchronization project. Two steps forward have occurred. The set-up Here is a brief recapitulation. Let G be a transitive permutation group on Ω, where |Ω| = n. We say that G is non-synchronizing if there … Continue reading →

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A mathematical promenade

Posted on 20/10/2018 by

I haven’t posted for a while; I have been in China where the firewall allows me to read WordPress but not to post. Normal service now resumed (hopefully). Given four real polynomials, all of which vanish at the origin, suppose … Continue reading →

Posted in books, exposition | Tagged , , , | 1 Comment