Counting Tripods on the Torus

TL;DR

This paper investigates the enumeration of specific immersed graphs called tripods on a flat torus, translating the problem into lattice point counting in complex space and providing asymptotic results.

Contribution

It introduces a novel approach to counting tripods on the torus by linking it to lattice point counting in complex Euclidean space.

Findings

Asymptotic count of tripods on the torus

Connection between geometric graph counting and lattice points

Application of lattice point counting techniques

Abstract

Motivated by the problem of counting finite BPS webs, we count certain immersed metric graphs, tripods, on the flat torus. Classical Euclidean geometry turns this into a lattice point counting problem in $\mathbb C^2$, and we give an asymptotic counting result using lattice point counting techniques.