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arXiv · 2304.03186

A counterexample to a conjecture on simultaneous Waring identifiability

Elena Angelini
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Abstract

The new identifiable case appeared in \cite{AGMO}, together with the analysis on simultaneous identifiability of pairs of ternary forms recently developed in \cite{BG}, suggested the following conjecture towards a complete classification of all simultaneous Waring identifiable cases: for any $ d \geq 2 $, the general polynomial vectors consisting of $ d-1 $ ternary forms of degree $ d $ and a ternary form of degree $ d+1 $, with rank $ \frac{d^2+d+2}{2} $, are identifiable over $ \mathbf{C} $. In this paper, by means of a computer-aided procedure inspired to the one described in \cite{AGMO}, we obtain that the case $ d = 4 $ contradicts the previous conjecture, admitting at least $ 36 $ complex simultaneous Waring decompositions (of length $ 11 $) instead of $ 1 $.

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Elena Angelini. 2023-04-06. A counterexample to a conjecture on simultaneous Waring identifiability. https://arxiv.org/abs/2304.03186

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