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Step growth polymerization involves bi or multifunctional monomers. Bifunctional monomers react to form linear step growth polymers, whereas multifunctional monomers react to form non-linear or branched polymers.
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Recurrence solution of monomer-polymer models on two-dimensional rectangular lattices.

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  • 1Department of Biostatistics, School of Public Health, <a href="https://ror.org/03v76x132">Yale University,</a> New Haven CT 06520, USA.

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Summary
This summary is machine-generated.

This study introduces a general method for counting polymer coverings on rectangular lattices. The findings reveal simple recurrence relations for polymer arrangements, offering potential insights into complex computational problems.

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Area of Science:

  • Statistical mechanics
  • Combinatorics
  • Computational complexity

Background:

  • Investigates counting polymer coverings on rectangular lattices.
  • Defines polymers as k adjacent lattice sites, with unoccupied sites as monomers.
  • Highlights the monomer-dimer problem (k=2) as a known computationally hard problem (#P complete).

Purpose of the Study:

  • To develop a general method for enumerating polymer coverings on 2D rectangular lattices.
  • To establish recurrence relations for polymer arrangements.
  • To explore potential solutions for #P-complete problems in lattice configurations.

Main Methods:

  • Mathematical modeling of polymer coverings on lattices.
  • Derivation of recurrence relations for polymer arrangements.
  • Analysis of the monomer-polymer model for arbitrary k and lattice width n.

Main Results:

  • Proved that the number of polymer arrangements satisfies simple recurrence relations.
  • Demonstrated the generality of these relations for arbitrary polymer length (k) and lattice width (n).
  • Established a connection between the general monomer-polymer model and the known monomer-dimer problem.

Conclusions:

  • The derived recurrence relations offer a novel approach to counting polymer configurations.
  • These findings may provide new avenues for tackling long-standing computational complexity problems.
  • The monomer-polymer model generalizes known lattice covering problems.