Lattices, graphs, and Conway mutation

The Conway-sloane Calculus for 2-adic Lattices

We develop the notational system developed by Conway and Sloane for working with quadratic forms over the 2-adic integers, and prove its validity. Their system is far better for actual calculations than earlier methods, and has been used for many years, but it seems that no proof has been published before now. Throughout, an integer means an element of the ring Z2 of 2-adic integers, and we wri...

Distributive Lattices from Graphs

Several instances of distributive lattices on graph structures are known. This includes c-orientations (Propp), α-orientations of planar graphs (Felsner/de Mendez) planar flows (Khuller, Naor and Klein) as well as some more special instances, e.g., spanning trees of a planar graph, matchings of planar bipartite graphs and Schnyder woods. We provide a characterization of upper locally distributi...

Probability on Graphs Random Processes on Graphs and Lattices

Concept Lattices of RDF Graphs

The concept lattice of an RDF graph is defined. The intents are described by graph patterns rather than sets of attributes, a view that is supported by the fact that RDF data is essentially a graph. A simple formalization by triple graphs defines pattern closures as connected components of graph products. The patterns correspond to conjunctive queries, generalization of properties is supported....

Lattices of Triadic Concept Graphs

Triadic concept graphs have been introduced as a mathema-tization of conceptual graphs with subdivision. In this paper it is shown that triadic concept graphs of a triadic power context family always form a complete lattice with respect to the generalization order. For stating this result, a clariication of the notion of generalization is needed. It turns out that the generalization order may b...