线性子移位的伊甸园定理
A Garden of Eden theorem for linear subshifts
摘要：
设$G$是顺从群，$V$是任意域$\K$上的有限维向量空间。证明了如果$X \subset V^G$是有限型强不可约线性子移位，$τ\colon X \to X$是线性元胞自动机，则$τ$是满射的当且仅当它是预内射的.证明了如果$G$是可数的，且$X \subset V^G$是强不可约线性子移位，则每个内射线性元胞自动机$τ\colon X \to X$都是满射的.
英文摘要：
Let $G$ be an amenable group and let $V$ be a finite-dimensional vector space over an arbitrary field $\K$. We prove that if $X \subset V^G$ is a strongly irreducible linear subshift of finite type and $τ\colon X \to X$ is a linear cellular automaton, then $τ$ is surjective if and only if it is pre-injective. We also prove that if $G$ is countable and $X \subset V^G$ is a strongly irreducible linear subshift, then every injective linear cellular automaton $τ\colon X \to X$ is surjective.
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