Recurrence solution of monomer-polymer models on two-dimensional rectangular lattices
<|reference_start|>Recurrence solution of monomer-polymer models on two-dimensional rectangular lattices: The problem of counting polymer coverings on the rectangular lattices is investigated. In this model, a linear rigid polymer covers $k$ adjacent lattice sites such that no two polymers occupy a common site. Those unoccupied lattice sites are considered as monomers. We prove that for a given number of polymers ($k$-mers), the number of arrangements for the polymers on two-dimensional rectangular lattices satisfies simple recurrence relations. These recurrence relations are quite general and apply for arbitrary polymer length ($k$) and the width of the lattices ($n$). The well-studied monomer-dimer problem is a special case of the monomer-polymer model when $k=2$. It is known the enumeration of monomer-dimer configurations in planar lattices is #P-complete. The recurrence relations shown here have the potential for hints for the solution of long-standing problems in this class of computational complexity.<|reference_end|>
@article{kong2024recurrence,
    title={Recurrence solution of monomer-polymer models on two-dimensional
  rectangular lattices},
    author={Yong Kong},
    journal={arXiv preprint arXiv:2405.09457},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.09457},
    primaryClass={cond-mat.stat-mech cs.CC math.CO}
}