A dimer covering of a finite graph is a set of edges joining distinct vertices such that every vertex is incident to exactly one selected edge. A dimer covering is therefore a perfect matching. On the square grid, dimer coverings are equivalent to domino tilings of the corresponding region. Weighted enumeration is expressed by the dimer partition function.
Dimer Covering
See also
Domino Tiling, Matching, Perfect MatchingExplore with Wolfram|Alpha
References
Kasteleyn, P. W. "The Statistics of Dimers on a Lattice: I. The Number of Dimer Arrangements on a Quadratic Lattice." Physica 27, 1209-1225, 1961. https://doi.org/10.1016/0031-8914(61)90063-5.Cite this as:
Weisstein, Eric W. "Dimer Covering." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DimerCovering.html