# Exact solution of a monomer-dimer problem: a single boundary monomer on a nonbipartite lattice.

@article{Wu2011ExactSO, title={Exact solution of a monomer-dimer problem: a single boundary monomer on a nonbipartite lattice.}, author={F. Y. Wu and W. J. Tzeng and Nickolay Sh. Izmailian}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2011}, volume={83 1 Pt 1}, pages={ 011106 } }

We solve the monomer-dimer problem on a nonbipartite lattice, a simple quartic lattice with cylindrical boundary conditions, with a single monomer residing on the boundary. Due to the nonbipartite nature of the lattice, the well-known method of solving single-monomer problems with a Temperley bijection cannot be used. In this paper, we derive the solution by mapping the problem onto one of closed-packed dimers on a related lattice. Finite-size analysis of the solution is carried out. We find…

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## References

SHOWING 1-10 OF 21 REFERENCES

Table of Integrals, Series, and Products

- Mathematics, Engineering
- 1943

Introduction. Elementary Functions. Indefinite Integrals of Elementary Functions. Definite Integrals of Elementary Functions. Indefinite Integrals of Special Functions. Definite Integrals of Special…

Phys

- Rev. E 74, 020104(R)
- 2006

Phys

- 110, 671
- 2003

in Combinatorics: Proceedings of the British Combinatorial Conference

- London Mathematical Society Lecture Notes Series, Vol. 13
- 1974

Phil

- Mag. 6, 1061
- 1961

Philos

- Mag. 6, 1061
- 1961

Phys

- Rev. 124, 1664
- 1961

Physica (Amsterdam) 27

- 1209
- 1961

Physica 27

- 1209
- 1961

Izmailian

- K. B. Oganesyan, and C.-K. Hu, Phys. Rev. E 67, 066114
- 2003