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# Tag Archives: semigroup

## Combinatorial Yang-Baxter, 2

It is five years since Tatiana Gateva-Ivanova introduced me to the combinatorial Yang–Baxter equation. I may be slow; I have just understood why this is a good thing for a mathematician to study, aside from its applications in physics (whatever … Continue reading

Posted in exposition
Tagged 2-dimensional semigroups, associative law, semigroup, Yang-Baxter equation
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## Definitions

Time to generalise from the preceding examples. There are several good reasons why a choice of definitions is a good thing. First, as several points in the discussion of graphs suggested, different definitions may be adapted for different kinds of … Continue reading

## Endomorphism monoids of graphs

A monoid is, for me, a set of mappings on a finite domain which is closed under composition and contains the identity mapping. The composition is, of course, associative. Thus, it is “a group without the inverses”. A homomorphism from … Continue reading

Posted in exposition, open problems
Tagged endomorphism monoid, grid graph, Latin square, semigroup
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## Primitivity

The first mathematics book that I read really seriously was Helmut Wielandt’s Finite Permutation Groups. So I have known the definition of a primitive permutation group for more than forty years. But there is still more to learn. My recent … Continue reading

Posted in exposition, open problems
Tagged graph, primitive group, semigroup, synchronization
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