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- W2055398825 abstract "A distributive lattice structure ${mathbf M}(G)$ has been established on the set of perfect matchings of a plane bipartite graph $G$. We call a lattice {em 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 ${mathbf M}(G)$ is irreducible. Based on this result, a decomposition theorem on MDLs is obtained: a finite distributive lattice $mathbf{L}$ is an MDL if and only if each factor in any cartesian product decomposition of $mathbf{L}$ is an MDL. Two types of MDLs are presented: $J(mathbf{m}times mathbf{n})$ and $J(mathbf{T})$, where $mathbf{m}times mathbf{n}$ denotes the cartesian product between $m$-element chain and $n$-element chain, and $mathbf{T}$ is a poset implied by any orientation of a tree." @default.
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- W2055398825 date "2014-03-01" @default.
- W2055398825 modified "2023-10-17" @default.
- W2055398825 title "Decomposition theorem on matchable distributive lattices" @default.
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- W2055398825 doi "https://doi.org/10.1016/j.dam.2013.09.008" @default.
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