Category Archives: open problems

unsolved mathematical problems

Chains of semigroups

Posted on 27/01/2015 by

I have written here about the lovely formula for the length of the longest chain of subgroups in the symmetric group Sn: take n, increase it by 50% (rounding up if necessary), subtract the number of ones in the base … Continue reading →

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A niggling problem

Posted on 24/01/2015 by

Preparing my talk for the Research Day, I was reminded of a problem I can’t solve, that has niggled me for many years. Maybe someone else can solve it, or maybe I will be encouraged to do it myself. Here … Continue reading →

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Bijective proofs

Posted on 04/01/2015 by

A fourth proof Last month I described three proofs of the formula for the number of ways to choose k objects from a set of n, if repetition is allowed and order is not significant; it is the same as … Continue reading →

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Three versus four

Posted on 27/11/2014 by

The title is homage to the Gödel’s Last Letter and P=NP blog, which a week ago had a post entitled Two versus three. At the problem session at the Banff meeting last night, Dugald Macpherson and Andras Pongracz posed various … Continue reading →

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9,21,27,45,81,153,…

Posted on 16/10/2014 by

This is the sequence of degrees of primitive groups which don’t synchronize a map of rank 3, equivalently graphs with clique number and chromatic number 3 having primitive automorphism groups. You could argue that the sequence should start with 3, … Continue reading →

Posted in doing mathematics, open problems | Tagged , , , , , | 2 Comments

Easy to state, hard to solve?

Posted on 31/07/2014 by

I described here how Pablo Spiga and I showed that all but finitely many nontrivial switching classes of graphs with primitive automorphism group contain a graph with trivial automorphism group, and found the six exceptions. (The trivial switching classes are … Continue reading →

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Categorification, step 1

Posted on 12/06/2014 by

Today at the St Petersburg meeting, Igor Frenkel talked about categorification. He explained that there are five levels (maybe more!) and one has to take certain steps between them; he illustrated with an example, where level 0 was Jacobi’s Triple … Continue reading →

Posted in exposition, open problems | Tagged , , , , , | 2 Comments