Subdivergence-free gluings of trees

TL;DR

This paper studies subdivergence-free gluings of rooted trees, motivated by quantum field theory, providing enumeration results, connections to permutations, and algorithms for computation.

Contribution

It introduces the concept of subdivergence-free gluings, explores their enumeration for specific tree families, and develops algorithms to compute them.

Findings

Enumeration of subdivergence-free gluings for certain tree families

Connection between gluings and connected permutations

Algorithms for computing subdivergence-free gluings

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.