论文标题
双线性图的生长
Growth of bilinear maps
论文作者
论文摘要
对于双线性地图$*：\ MATHBB r^d \ times \ Mathbb r^d \ to \ Mathbb r^d $的非负系数和一个vector $ s \ in \ mathbb r^d $ in \ mathbb r^d $的积极条目，包括$ n $ n $ n $ n $ n $ n $ n $*的方式输入所有结果向量。渐近行为是，当$ n $倾向于无穷大时，此最大入口的$ n $ Th root会收敛到增长率$λ$。在本文中，我们通过称为线性模式的特殊结构证明了这种限制的存在。我们还提出了一个问题，即结构与$λ$之间存在关系的可能性。
For a bilinear map $*:\mathbb R^d\times \mathbb R^d\to \mathbb R^d$ of nonnegative coefficients and a vector $s\in \mathbb R^d$ of positive entries, among an exponentially number of ways combining $n$ instances of $s$ using $n-1$ applications of $*$ for a given $n$, we are interested in the largest entry over all the resulting vectors. An asymptotic behavior is that the $n$-th root of this largest entry converges to a growth rate $λ$ when $n$ tends to infinity. In this paper, we prove the existence of this limit by a special structure called linear pattern. We also pose a question on the possibility of a relation between the structure and whether $λ$ is algebraic.
