Geodesic
Combinatorial aspects of the dimer problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 31 (1977) no. 1, pp. 89-100

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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. 
@article{TMF_1977_31_1_a8,
     author = {V. B. Priezzhev},
     title = {Combinatorial aspects of the dimer problem},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {89--100},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1977_31_1_a8/}
}
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V. B. Priezzhev. Combinatorial aspects of the dimer problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 31 (1977) no. 1, pp. 89-100. http://geodesic.mathdoc.fr/item/TMF_1977_31_1_a8/