Polymer adsorption, Dyck paths and a little number theory.

Andrew Rechnitzer
(York Univ.)

One of the many places in which lattice animals and their relatives arise
is in the modelling of the physical properties of polymers. Most work
in this area has concentrated on polymers made up of a single type
of building block (or monomer), and many results (both exact and
numerical) are known.

Not all polymers are homogeneous, and many interesting polymers (such as
DNA) are made up of two or more types of monomers with different
properties. There are far fewer exact results for models of inhomogeneous
polymers (or co-polymers)  and many basic questions about their behaviour
remain unanswered.

I will give a LIGHT introduction to some basic statistical mechanics and
phase transitions, before proceeding onto some combinatorial models of
polymers, some recent exact solutions, and the application of a little
number theory.