Biased graphs. VI. synthetic geometry

Synthetic Cevian Geometry Synthetic Cevian Geometry 1

Biased Graphs

Biased Graphs . Iv

Constructive Synthetic Geometry

In the current problem set we are investigating two problems in computational geometry using concepts from our study of the computable real numbers and calculus. The main problem we are examining is the notion of a set of points in the plane and how to compute their convex hull. In the last lecture we briefly discussed how it is possible to investigate computational geometry in a more abstract ...

Biased graphs IV: Geometrical realizations

A gain graph is a graph whose oriented edges are labelled invertibly from a group G, the gain group. A gain graph determines a biased graph and therefore has three natural matroids (as shown in Parts I–II): the bias matroid G has connected circuits; the complete lift matroid L0 and its restriction to the edge set, the lift matroid L, have circuits not necessarily connected. We investigate repre...