Labeling and ordering the paths

Abstract

Smaller model spaces, i.e spaces of a smaller number of orbitals n′ ≤ n or particles, N′ ≤ N, are represented by subgraphs embedded in a natural way in G₂(2n: N), with (N′,2n′) vertex as their tail. Similarly one can imagine larger graphs in which G₂(2n: N) is embedded. Description of the borders of a graph is simpler if we regard vertices and arcs of these larger graphs as ‘virtually present’: existing, but giving a null contribution to the real graph. The fixed-slope graphs, by virtue of this embedding property, admit a natural ordering of paths.