HUJI Combinatorics Seminar 


When: Monday Jan 18th, 2021, at 11AM (Israel time)


Zoom link: https://huji.zoom.us/j/81176578450?pwd=TStYWHhhWnE3YkNuR0RlZmkrejBIUT09



Speaker: Shin-ichi Tanigawa (University of Tokyo)


Title: Maximal Matroid Problem on Graphs

Abstract: 
The problem of characterizing the 3-dimensional generic rigidity of graphs is one of the major open problems in graph rigidity theory. Walter Whiteley conjectured that the 3-dimensional generic matroid coincides with a matroid studied in the context of bivariate splines.  In this talk I will show a solution to the characterization problem for the latter matroid. 
I will explain the idea of our characterization from the view point of constructing maximal matroids on complete graphs. Specifically, for a graph H, a matroid on the edge set of a complete graph is called a H-matroid if every edge set of each subgraph isomorphic to H is a circuit. A main theme of my talk will be about identifying and constructing a maximal H-matroid with respect to the weak order. 
This talk is based on a joint work with Bill Jackson and Katie Clinch.