The Waring rank of binary binomial forms

TL;DR

This paper provides an explicit formula for calculating the Waring rank of binary binomial forms with complex coefficients, including examples and comparisons with real Waring ranks.

Contribution

It introduces a new explicit formula for the Waring rank of binary binomial forms, advancing understanding of their algebraic complexity.

Findings

Explicit formula for complex Waring rank of binary binomials

Examples illustrating the formula's application

Comparison between complex and real Waring ranks

Abstract

We give an explicit formula for the Waring rank of every binary binomial form with complex coefficients. We give several examples to illustrate this, and compare the Waring rank and the real Waring rank for binary binomial forms.