Applied Algebra Seminar

York University - Fall 2002

October 28, 2002 - 4:30pm
Ross N638

Speaker: Jeremy Martin

University of Minnesota



Pictures of the Complete Graph



A picture of the complete graph K_n consists of n labelled points in the plane, connected with (n choose 2) lines. I'm going to talk about the algebraic relations that must hold among the slopes of these lines. This sounds like a problem in classical geometry, but it turns out that the tools to attack it come from combinatorics. First, the equations defining a picture can be described using the theory of combinatorial rigidity of graphs. Second, once one knows what these equations are, one can apply another combinatorial idea, the theory of Stanley-Reisner rings, to obtain geometric invariants of the space of all solutions. Finally, various sorts of labelled trees play important roles in describing these invariants combinatorially.



Algebra Seminar Home - Fall 2002