Algebraic Combinatorics Seminar - Clair Dai

Title: Counting subdivergence-free gluing of trees

Abstract:

If we take two rooted trees with the same number of leaves and form a graph by gluing the leaves of one tree to the other, then we say the graph is subdivergence-free if no 2-edge cut have been generated. We are interested in counting the number of ways to do this and will discuss some special cases where we can obtain some enumerative results. The problem is motivated by the study of primitive Feynman diagrams with cuts, and how they can be recreated from the cut piece.