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.

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