I went to this conference in Dunedin just for the first two days – it ends on 20 June.

A lot of good generating functions arise from the enumeration of permutations avoiding certain patterns. The plenary talk by Mireille Bousquet-Melou (whose talks are always a model of clarity) discussed the systematic solution of various functional equations arising from fairly straightforward recursive decompositions of these combinatorial classes. As well as the by now traditional kernel method, she discussed the “algebraic kernel method” which uses symmetries of the kernel function to derive a system of equations that is amenable to simplification.

I have been thinking for a long time about the need for a better presentation of the kernel method in these contexts. Perhaps this will finally inspire me to write something.