Year: 2026
Type: preprint
Abstract: For a third-order symmetric tensor, the Comon rank gap is the difference between its CP rank and its symmetric rank. We study direct sums of Lovitz's rational $27$-dimensional tensor, whose two ranks are $55$ and $56$. Two copies have ranks $110$ and $112$, and three copies have ranks $165$ and $168$, over both the real and the complex fields. Thus direct sums yield concise cubic tensors on spaces of dimensions $54$ and $81$ with Comon rank gaps two and three.
Source: arXiv (Cornell University)
Author: Li, Jianze
Language: English
Subfield: Computational Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215718415