International conference
Combinatorial Methods in Physics and Knot Theory

The clover-leaf structures under discussion are defined as follows. The polymer is supposed to bear numerous sticky centers along the chain, these centers being capable of forming thermoreversible bonds with each other. One can represent this polymer as a line with some active points on it. Then the aforementioned thermoreversible bonds can be represented as additional (say, dashed) arch lines connecting some of the active points. Now, we say that some given structure belongs to the clover-leaf type if the archs on the corresponding diagram do not intersect each other. One can easily see that a spatial representation of such structures is nothing else but a tree-like ierarchy of simple circles. The motivation to study these systems is mostly biological, as RNA molecules are known to form such structures. To describe the system under consideration we use a formalism based on a Dyson equation. I'm going to show how this equation is solved in the simplest case, when all the sticky centers are identical (we call this case homopolymer), distances between them are equal and there is no external field. I will briefly discuss also two more complicated cases: i) adsorption-desorption transition of a homopolymer forming clover-leaf structures on a delta-functional potential well (the possibility that a reentrant desorption-adsorption-desorption phase transition may arise will be shown), and ii) the bulk behaviour of a regular heteropolymer with two different types of sticky centers, capable of forming alternating bonds only.