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# Tag Archives: groups

## Graphs on groups, 3

Since this stuff keeps growing, I have decided to keep the most recent version on the web. It is now nearly twice as long as the first version I circulated. If you are interested, please take a copy: it’s at … Continue reading

## G2D2, 1: setting the scene

I’m in Yichang, at the China Three Gorges University, for the conference and summer school G2D2 (“Groups and graphs, designs and dynamics”). This is the sixth meeting in the series: the previous ones were G2C2: Groups and graphs, cycles and … Continue reading

Posted in exposition, history, Uncategorized
Tagged designs, dynamics, G2 conferences, graphs, groups, Hangzhou, Three Gorges University, Yichan, Zhejiang University
1 Comment

## Normal

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

Posted in exposition
Tagged Cayley graphs, field extensions, groups, matrices, terminology, topological spaces
3 Comments

## BCC, day 2

There was a London Mathematical Society regional meeting in the University of Warwick today, to be followed by a workshop on finite simple groups to celebrate the birthday of Richard Lyons, one of the pioneers and heroes of the Classification. … Continue reading

Posted in events
Tagged automorphisms, Colva Roney-Dougal, groups, Ian Wanless, Nature, quasigroups, Robert Guralnick, Stefanie Gerke, Tomasz Luczak
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## OuLiPo

OuLiPo, or Ouvroir de Littérature Potentielle (which they translate as “Charity bazaar of potential literature”) were a collection of writers I knew little about until yesterday. I knew a couple of things: Martin Gardner wrote about them, mentioning among other … Continue reading

Posted in mathematics and ...
Tagged Claude Berge, combinations, games, Georges Perec, graphs, groups, literature, orthogonal Latin squares, permutations, Pierre Rosenstiehl
3 Comments

## 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

Posted in exposition
Tagged entropy, groups, information, random variables, Shannon, subgroups, Terence Chan
1 Comment

## Lecture notes

I have decided to follow Dima’s suggestion and post my collection of lecture notes here. You will find them from the page “Lecture notes” on the menu bar at the bottom of the picture at the top of the blog. … Continue reading

Posted in Lecture notes
Tagged abstract algebra, combinatorics, enumerative combinatorics, groups, linear algebra, number theory, probability, rings
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## Transitivity and synchronization

Let Sn be the symmetric group of all permutations of {1,…,n}, and Tn the full transformation monoid of all functions from this set to itself. Recently I have come to the meta-conjecture that there is a fairly close analogy between … Continue reading

Posted in exposition, open problems
Tagged Dixon's theorem, endomorphisms, graphs, groups, semigroups, synchronization, synchronizing monoids
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## Groups with unique involution

I discussed the binary polyhedral groups in the second post on the ADE diagrams. A more general class of groups has cropped up a couple of times recently, namely finite groups containing a unique involution. I’d like to discuss them … Continue reading