3 problems

Let $d\ge2$ be a positive integer and let $R$ be a non-empty family of partitions on $\lbrack d\rbrack$. For every positive integer $l$, let $\operatorname{\mathit{R}rk}$ denote th…

Let $d\ge2$ be an integer and let $R$ be a non-empty family of partitions on $\lbrack d\rbrack$. Let $\operatorname{\mathit{R}rk}$ denote the rank associated with $R$. Linear bound…

Let $d \ge 2$, $s \ge 1$ be positive integers and let $R$ be a non-empty family of partitions on $\lbrack d \rbrack$. For order-$d$ tensors $T_1,\dots,T_s$ and $a\in\mathbb{F}^s$,…