Seminar Details

A plane tree is a rooted tree where each node's children have a left-to-right order. Classically, the number of plane trees with n+1 vertices is equal to the nth Catalan number. We can generalize this basic enumeration problem to plane trees with colored vertices. We consider coloring rules that, given the color of the parent node, restrict the choices of how to color the children. This general framework is fertile ground for combinatorial exploration. For one thing, it generalizes many different examples that have been studied in the literature. It also leads to many new results, including bijections with other known problems. In this talk, we will explore various families of coloring rules and explore the integer sequences that enumerate plane trees colored according to those rules. This is joint work with Stoyan Dimitrov, Kimberly Hadaway, Ashley Tharp, and Stephan Wagner.