A dimer covering of a finite graph is a set of edges incident to every vertex exactly once, and hence is 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." Physica 27, 1209-1225, 1961.Cite this as:
Weisstein, Eric W. "Dimer Covering." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DimerCovering.html