The Waring Rank of Ternary Cubic Forms
Gary Brookfield
TL;DR
This paper establishes specific coefficient-based conditions that determine the Waring rank of ternary cubic forms, advancing understanding of their algebraic structure.
Contribution
It introduces new coefficient conditions that precisely determine the Waring rank of ternary cubic forms, a novel characterization in algebraic geometry.
Findings
Derived explicit coefficient conditions for Waring rank
Characterized rank 3 and 4 forms in ternary cubics
Provided a classification framework for these forms
Abstract
We provide conditions on the coefficients of a ternary cubic form that determine its Waring rank.
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Taxonomy
TopicsTensor decomposition and applications · Advanced Algebra and Geometry · Finite Group Theory Research