Functional clones and expressibility of partition functions

We study functional clones, which are sets of non-negative pseudo-Boolean functions (functions {0,1}k→R≥0) closed under (essentially) multiplication, summation and limits. Functional clones naturally form a lattice under set inclusion and are closely related to counting Constraint Satisfaction Problems (CSPs). We identify a sublattice of interesting functional clones and investigate the relationships and properties of the functional clones in this sublattice.