Symmetry Breaking in Graphs and Matroids

Document Type

Presentation Abstract

Presentation Date

10-12-2009

Abstract

"What can we do to an object to break its symmetry?" That is, how can we restrict the object in some way so that the only automorphism is trivial? We examine two approaches. The first involves distinguishing the elements of the object while the second involves fixing some of the elements. Distinguishing and fixing numbers were originally defined for graphs. We are interested in the extension of these ideas to matroids. The talk will begin with a survey of graph results. Next, matroids will be introduced, and the concept of a matroid automorphism defined. (Familiarity with matroids will not be assumed; all matroids in the talk can be visualized as a graph or geometry.) Lastly, we give a sampling of fixing and distinguishing number results for matroids.

Additional Details

Monday, 12 October 2009
3:10 p.m. in Math 103
4:00 p.m. Refreshments in Math Lounge 109

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