Abstract:
A n-dimensional problem of enumeration is formulated and solved exactly for one
class of dimer configurations. Enumerated dimer configurations satisfy the standard
restrictions of the dimer problem as well as the additional condition of the absence
of any closed path in the corresponding graph representation. The equivalence of the
problem considered to the standard dimer problem for two-dimensional lattice is established
rigorously.
\Bibitem{Pri77}
\by V.~B.~Priezzhev
\paper Combinatorial aspects of the dimer problem
\jour TMF
\yr 1977
\vol 31
\issue 1
\pages 89--100
\mathnet{http://mi.mathnet.ru/tmf2939}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=523378}
\transl
\jour Theoret. and Math. Phys.
\yr 1977
\vol 31
\issue 1
\pages 337--345
\crossref{https://doi.org/10.1007/BF01041240}
Linking options:
https://www.mathnet.ru/eng/tmf2939
https://www.mathnet.ru/eng/tmf/v31/i1/p89
This publication is cited in the following 8 articles:
E. I. Kornilov, V. B. Priezzhev, “Exactly solvable lattice model of rooted branched polymers”, Theoret. and Math. Phys., 98:1 (1994), 61–71
E. I. Kornilov, A. A. Litvin, “On the entropy contribution to thermodynamics of melted flux liquids”, Z. Physik B - Condensed Matter, 84:1 (1991), 3
E. I. Kornilov, V. B. Priezzhev, “Generalized bethe approximation in lattice models of long polymers”, Z. Physik B - Condensed Matter, 54:4 (1984), 351
V. B. Priezzhev, “The statistics of dimers on a three-dimensional lattice. I. An exactly solvable model”, J Stat Phys, 26:4 (1981), 817
N. D. Gagunashvili, V. B. Priezzhev, “Thermodynamic properties of polymer mixtures on a plane square lattice”, Theoret. and Math. Phys., 45:2 (1980), 1017–1021
N. D. Gagunashvili, V. B. Priezzhev, “Close packing of rectilinear polymers on a square lattice”, Theoret. and Math. Phys., 39:3 (1979), 507–510
V B Priezzhev, “Series expansion for rectilinear polymers on the square lattice”, J. Phys. A: Math. Gen., 12:11 (1979), 2131
V. B. Priezzhev, “Model of monomers and dimers with interaction”, Theoret. and Math. Phys., 36:1 (1978), 634–638
Citation in format AMSBIB
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