Combinatorics Seminar: Oriented Matroids

Abstract: How can you express the notion of oriented matroids without any of the orientation definitions and properties? This talk aims to explicitly describe the relationship between oriented matroids and their non-oriented counterparts. Using a result from a paper on unique L-infinity nearest points (Bernstein and Long, 2017), I will describe how to redo the results in the plain language of non-oriented matroids, specifically by introducing the defining characteristics of oriented matroids and their geometric interpretations. I will also introduce new definitions of non-oriented matroid properties and show why they are useful tools to reconstruct the proof. These new insights aim to help prove the uniqueness of L-1 nearest points.

Host: Martha Precup