Subdivergence-free gluings of trees

Abstract

A gluing of two rooted trees is an identification of their leaves and un-subdivision of the resulting 2-valent vertices. A gluing of two rooted trees is subdivergence free if it has no 2-edge cuts with both roots on the same side of the cut. The problem and language is motivated by quantum field theory. We enumerate subdivergence-free gluings for certain families of trees, showing a connection with connected permutations, and we give algorithms to compute subdivergence-free gluings.

minor edits according to referee comments, 20 pages

References in corpus (4)

• Hopf Algebras, Renormalization and Noncommutative Geometry
• Mating of trees for random planar maps and Liouville quantum gravity: a survey
• Cutkosky Rules and Outer Space
• Algebraic Interplay between Renormalization and Monodromy

Cited by in corpus (1)

• Algebraic Interplay between Renormalization and Monodromy