2008/07/08 by Stefan Felsner, S. Felsner, Felsner, S. +3
Computer Science · Mathematics · #05C20 #05C38 #06B15 #06D99 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.CO #msc:05C20 #msc:05C38 #msc:06B15 #msc:06D99 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0807.1217
15 pages, 5 figures
arxiv created 2008/07/08 · openalex publication_date 2008/07/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.