## Lattice animals; why can't we solve any of these things

### Andrew Rechnitzer, (University of Melbourne)

Abstract: The enumeration of lattice animals is (perhaps) one of the
most famous problems in combinatorics, and as a lattice model of polymers
it is also of considerable importance in statistical physics and
theoretical chemistry. Though lattice animals have been studied since the
40's, it is surprising how few rigorous results exist.

In this talk I will explore one possible reason for this --- that the
model is not solvable in terms of the most common functions of
mathematical physics, "differentiably finite" functions.

The proof of this relies on (almost) purely combinatorial and graphical
techniques which demonstrate a direct relationship between the types of
graph structures within the bond animals to the singularities of the
solution.

Applied Algebra seminar home