Enumerative combinatorics
Introduction to graph theory
Z-transformation graphs of perfect matchings of hexagonal systems
Discrete Mathematics - First Japan Conference on Graph Theory and Applications
The lattice structure of flow in planar graphs
SIAM Journal on Discrete Mathematics
Hexagonal systems with forcing edges
Discrete Mathematics
The connectivity of Z-transformation graphs of perfect matchings of polyominoes
Discrete Mathematics
Plane elementary bipartite graphs
Discrete Applied Mathematics
On the Structure of Some Spaces of Tilings
SIAM Journal on Discrete Mathematics
Coding distributive lattices with edge firing games
Information Processing Letters
Resonance graphs of catacondensed even ring systems are median
Discrete Mathematics
Combinatorics of perfect matchings in plane bipartite graphs and application to tilings
Theoretical Computer Science - Special issue: Tilings of the plane
The lattice structure of the set of domino tilings of a polygon
Theoretical Computer Science - Discrete applied problems, florilegium for E. Goles
Resonance Graphs and a Binary Coding for the 1-Factors of Benzenoid Systems
SIAM Journal on Discrete Mathematics
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A distributive lattice structure M(G) has been established on the set of perfect matchings of a plane bipartite graph G. We call a lattice matchable distributive lattice (simply MDL) if it is isomorphic to such a distributive lattice. It is natural to ask which lattices are MDLs. We show that if a plane bipartite graph G is elementary, then M(G) is irreducible. Based on this result, a decomposition theorem on MDLs is obtained: a finite distributive lattice L is an MDL if and only if each factor in any cartesian product decomposition of L is an MDL. Two types of MDLs are presented: J(mxn) and J(T), where mxn denotes the cartesian product between m-element chain and n-element chain, and T is a poset implied by any orientation of a tree.