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# Tag Archives: Dixon’s theorem

## 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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## The symmetric group, 11

I am going to talk about a celebrated theorem of John Dixon and some of its variants; this is on my mind at the moment, for reasons I will explain at the end. Dixon’s theorem is easily stated. Two random … Continue reading

Posted in exposition, symmetric group, synchronization
Tagged Baire category, Dixon's theorem, symmetric group
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