The Degree of a Tropical Root Surface of Type $A$

TL;DR

This paper proves a formula for the degree of the tropical surface associated with the root system A_{n-1}, revealing a precise mathematical relationship.

Contribution

It establishes the exact degree of the tropical surface for the root system A_{n-1}, a new result in tropical geometry.

Findings

Degree of tropical surface for A_{n-1} is (1/2)n(n-1)(n-2)

Provides a closed-form formula for the degree

Advances understanding of tropical surfaces in root systems

Abstract

We prove that the tropical surface of the root system $A_{n-1}$ has degree $\frac{1}{2}n (n-1)(n-2)$.