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# Tag Archives: vector spaces

## 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

## Steiner systems

Following Peter Keevash’s asymptotic existence proof for Steiner systems, does anything remain to be done? I would say yes, it certainly does; here are a few thoughts about the open problems in this area. Existence We are looking for a … Continue reading

## Automorphisms of groups

I set a question to my group theory class. It is quite easy until suddenly you find yourself falling off a cliff into deep water. Indeed, I don’t know the answer to the second part of this question. Show that … Continue reading

Posted in exposition, open problems
Tagged automorphism, Axiom of Choice, MathOverflow, vector spaces
4 Comments

## Bases

Sometimes you have to make things more complicated in order to make them simpler. My old friend Aiden Bruen visited this week, and told me about a paper by him and his son Trevor which has just appeared in the … Continue reading

Posted in exposition, mathematics, open problems
Tagged graphs, matroids, vector spaces
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