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arXiv · 2310.11356

The interplay between bounded ranks of tensors arising from partitions

Thomas Karam
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Abstract

Let $d \ge 2, h \ge 1$ be integers. Using a fragmentation technique, we characterise $(h+1)$-tuples $(R_1, \dots, R_h, R)$ of non-empty families of partitions of $\{1, \dots, d\}$ such that it suffices for an order-$d$ tensor to have bounded $R_i$-rank for each $i=1,\dots,h$ for it to have bounded $R$-rank. On the way, we prove power lower bounds on products of identity tensors that do not have rank $1$, providing a qualitative answer to a question of Naslund.

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Thomas Karam. 2023-10-17. The interplay between bounded ranks of tensors arising from partitions. https://arxiv.org/abs/2310.11356

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