منابع مشابه
A Variational Principle for Domino Tilings
1.1. Description of results. A domino is a 1×2 (or 2×1) rectangle, and a tiling of a region by dominos is a way of covering that region with dominos so that there are no gaps or overlaps. In 1961, Kasteleyn [Ka1] found a formula for the number of domino tilings of an m × n rectangle (with mn even), as shown in Figure 1 for m = n = 68. Temperley and Fisher [TF] used a different method and arrive...
متن کاملA Reciprocity Theorem for Domino Tilings
(Dated: April 30, 2001) Let T (m;n) denote the number of ways to tile an m-by-n rectangle with dominos. For any fixed m, the numbers T (m;n) satisfy a linear recurrence relation, and so may be extrapolated to negative values of n; these extrapolated values satisfy the relation T (m; 2 n) = εm;nT (m;n), where εm;n = 1 if m 2 (mod 4) and n is odd and where εm;n = +1 otherwise. This is equivalent ...
متن کاملDomino Tilings of a Checkerboard
for n ≥ 2, it can be shown that fn counts the number of ways to tile a 1 × n board with squares and dominoes. This interpretation of the Fibonacci numbers admits clever counting proofs of many Fibonacci identities. When we consider more complex combinatorial objects, we find that simply counting the number of tilings is not quite enough, and that we must consider instead weighted tilings. For e...
متن کاملSpaces of Domino Tilings
We consider the set of all tilings by dominoes (2 1 rectangles) of a surface, possibly with boundary, consisting of unit squares. Convert this set into a graph by joining two tilings by an edge if they diier by a ip, i.e., a 90 rotation of a pair of side-by-side dominoes. We give a criterion to decide if two tilings are in the same connected component, a simple formula for distances and a metho...
متن کاملDomino Tilings with Barriers
In this paper, we continue the study of domino-tilings of Aztec diamonds. In particular, we look at certain ways of placing ``barriers'' in the Aztec diamond, with the constraint that no domino may cross a barrier. Remarkably, the number of constrained tilings is independent of the placement of the barriers. We do not know of a simple combinatorial explanation of this fact; our proof uses the J...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2000
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-00-00355-6