Action graphs and Catalan numbers

Start: 03/04/2015 - 4:15pm
End  : 03/04/2015 - 5:15pm


Julie Bergner, University of California, Riverside


Action graphs are labeled directed graphs that arose in the study of group actions on other algebraic objects. The 0th action graph consists of a vertex and no edges, and new vertices and edges are added at each stage by an inductive process. We will prove that the number of new vertices (and edges) given at the nth step is given by the nth Catalan number. We will then give a direct comparison between these action graphs and planar rooted trees, which give another known method for producing Catalan numbers. Lastly, we will look at the motivation for defining action graphs and some of their generalizations. This work was done in collaboration with P. Hackney, G. Alvarez, and R. Lopez.

Shanahan Center for Teaching and Learning (SCTL), at Harvey Mudd, Basement, B460

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