Geodesic
Combinatorial aspects of the dimer problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 31 (1977) no. 1, pp. 89-100 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {1977},
     volume = {31},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1977_31_1_a8/}
}
TY  - JOUR
AU  - V. B. Priezzhev
TI  - Combinatorial aspects of the dimer problem
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1977
SP  - 89
EP  - 100
VL  - 31
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1977_31_1_a8/
LA  - ru
ID  - TMF_1977_31_1_a8
ER  - 
%0 Journal Article
%A V. B. Priezzhev
%T Combinatorial aspects of the dimer problem
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1977
%P 89-100
%V 31
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1977_31_1_a8/
%G ru
%F TMF_1977_31_1_a8
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/

[1] R. H. Fowler, G. S. Rushbrooke, Trans. Faraday Soc., 33 (1937), 1272 | DOI

[2] O. L. Heilman, E. H. Lien, Commun. Math. Phys., 25 (1972), 190 | DOI | MR | Zbl

[3] P. W. Kasteleyan, Physica, 27 (1961), 1209 | DOI

[4] H. N. V. Temperley, M. E. Fisher, Phil. Mag., 6 (1961), 1061 | DOI | MR | Zbl

[5] A. N. Zykov, Teoriya konechnykh grafov, «Nauka», 1969 | MR

[6] F. Khartri, Teoriya grafov, «Mir», 1973 | MR

[7] C. Domb, Adv. Phys., 9:34 (1960), 149 | DOI

[8] S. Sherman, J. Math. Phys., 1 (1960), 202 | DOI | MR

[9] L. D. Landau, E. M. Lifshits, Statisticheskaya fizika, «Nauka», 1964 | Zbl

[10] M. Kholl, Kombinatorika, «Mir», 1970 | MR

[11] T. H. Berlin, M. Kac, Phys. Rev., 86 (1952), 821 | DOI | MR | Zbl

[12] E. V. Montroll, Prikladnaya kombinatornaya matematika, Sb., «Mir», 1968