REMARK ON THE DIMER PROBLEM

被引：29

作者：

SACHS, H ^{[1
]}

ZERNITZ, H ^{[1
]}

机构：

[1] ARCOMP GMBH,ARNSTADT,GERMANY

来源：

DISCRETE APPLIED MATHEMATICS | 1994年 / 51卷 / 1-2期

关键词：

D O I：

10.1016/0166-218X(94)90106-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let S(n) be the 2n x 2n square lattice and c(S(n)) the number of dimer coverings of S(n). In 1961, M.E. Fisher, P.W. Kasteleyn and H.N.V. Temperley/M.E. Fisher established the-now classical-result that log c(S(n)) is asymptotically equivalent to C(S)\S(n)\ where C(S) > 0 is a constant. In this paper, another sequence {T(n)} of subsets of the infinite square lattice is considered which, in a way, is similar to {S(n)}, and by elementary means it is shown that the asymptotic behaviour of c(T(n)) is quite different from that of c(S(n)): in fact, log c(T(n)) approximately CT square-root \T(n)\ where C(T) > 0 is a constant.

引用

页码：171 / 179

页数：9

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