ULD-Lattices and Delta-Bonds

Details ULD-Lattices and Delta-Bonds ULD-Lattices and Delta-Bonds

2008-07-08

arxiv.org/abs/0807.1217v1

Mathematics

Combinatorics

15 pages, 5 figures

Scientific paper

We provide a characterization of upper locally distributive lattices (ULD-lattices) in terms of edge colorings of their cover graphs. In many instances where a set of combinatorial objects carries the order structure of a lattice this characterization yields a slick proof of distributivity or UL-distributivity. This is exemplified by proving a distributive lattice structure on Delta-bonds with invariant circular flow-difference. This instance generalizes several previously studied lattice structures, in particular, c-orientations (Propp), alpha-orientations of planar graphs (Felsner, resp. de Mendez) and planar flows (Khuller, Naor and Klein). The characterization also applies to other instances, e.g. to chip-firing games.

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