8th November 2005<br>
Peter Cameron (Queen Mary, Univ London).
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Orbit-counting for colourings, flows, and weight enumerators.
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The Tutte polynomial of a matroid has many specialisations which count
proper colourings or nowhere-zero flows of a graph, the weight
enumerator
of a linear code, etc. Given a group of automorphisms, we aim to produce
a polynomial which has similar specialisations to count orbits of the
group
on colourings, flows, etc. Such a polynomial can be defined for certain
matroids (those representable over principal ideal domains). Many
questions
about its properties are still open.