MULTIVARIATE EXPANSIVITY THEORY
Theophilus Agama · viXra · 2021
In this paper we launch an extension program for single variable expansivity theory. We study this notion under tuples of polynomials belonging to the ring $\mathbb{R}[x_1,x_2,\ldots,x_n]$. As an application we show that \begin{align}\mathrm{min}\{\mathrm{max}\{\mathrm{Ind}_{f_k}(x_{\sigma(i)})\}_{k=1}^{s}+1\}_{i=1}^{l}&<\frac{1}{l}\sum \limits_{i=1}^{l}\mathrm{max}\{\mathrm{Ind}_{f_k}(x_{\sigma(i)})\}_{k=1}^{s}+2+\mathcal{J} onumber \end{align}where $\mathcal{J}:=\mathcal{J}(l)\geq 0$ and $\mathrm{Ind}_{f_k}(x_j)$ is the largest power of $x_j$~($1\leq j\leq n$) in the polynomial $f_k\in \mathbb{R}[x_1,x_2,\ldots,x_n]$.