2023/04/06 by Elena Angelini, Angelini, Elena
Computer Science · Mathematics · #13P05 #14N05 #14N07 #14Q20 #15A69 #15A72 #65H10 #Algebraic Geometry (math.AG) #Algorithms and Data Compression #Coding theory and cryptography #FOS: Mathematics #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2304.03186
openalex publication_date 2023/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The new identifiable case appeared in \citeAGMO, together with the analysis on simultaneous identifiability of pairs of ternary forms recently developed in \citeBG, suggested the following conjecture towards a complete classification of all simultaneous Waring identifiable cases: for any d ≥ 2 , the general polynomial vectors consisting of d-1 ternary forms of degree d and a ternary form of degree d+1 , with rank (d2+d+2)/(2) , are identifiable over C . In this paper, by means of a computer-aided procedure inspired to the one described in \citeAGMO, 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 .