Regular structures of an intractable enumeration problem: a diagonal recurrence relation of monomer-polymer coverings on two-dimensional rectangular lattices (opens in new tab)

arXiv:2411.04147v2 Announce Type: replace-cross Abstract: In the monomer-polymer model, a linear rigid polymer covers $k$ adjacent lattice sites, with no lattice site occupied by more than one polymer. The polymers are called $k$-mers, and those unoccupied lattice sites are called monomers. The well-known monomer-dimer model is a special case of the monomer-polymer model with $k=2$. The enumeration of polymer coverings on two-dimensional rectangular lattices is considered as "intractable". We...