论文标题
在可数组上寻找亚班的生长和熵的下限
Finding lower bounds on the growth and entropy of subshifts over countable groups
论文作者
论文摘要
我们基于一个简单的条件，对定义该子迁移的一组禁止模式的简单条件给出了下班的生长。 Aubrun等。基于Lovász局部引理显示了类似的结果，用于对任何可数群体的次要转移，而Bernshteyn扩展了他们推断出对亚转移指数增长的下限。但是，我们的结果具有更简单的证据，更易于用于应用程序，并且可以从其文章中的应用程序上提供更好的界限（尽管尚不清楚我们的结果通常更强大）。 在$ \ mathbb {z} $上的亚转移的特定情况下，米勒给出的类似但较弱的状况暗示着相关的偏移。帕夫洛夫使用相同的方法提供了暗示指数增长的条件。我们为这种特定环境提供了结果的版本，并且证明它比Pavlov的结果和Miller的结果（实际上可以导致应用程序的大幅改进）更严格。 我们还将两个结果应用于几个不同的问题，包括强烈的基础缩影，非竞争性次要换档和kolmogorov子缩影的复杂性。
We give a lower bound on the growth of a subshift based on a simple condition on the set of forbidden patterns defining that subshift. Aubrun et Al. showed a similar result based on the Lovász Local Lemma for subshift over any countable group and Bernshteyn extended their approach to deduce, amongst other things, some lower bound on the exponential growth of the subshift. However, our result has a simpler proof, is easier to use for applications, and provides better bounds on the applications from their articles (although it is not clear that our result is stronger in general). In the particular case of subshift over $\mathbb{Z}$ a similar but weaker condition given by Miller was known to imply nonemptiness of the associated shift. Pavlov used the same approach to provide a condition that implied exponential growth. We provide a version of our result for this particular setting and it is provably strictly stronger than the result of Pavlov and the result of Miller (and, in practice, leads to considerable improvement in the applications). We also apply our two results to a few different problems including strongly aperiodic subshifts, nonrepetitive subshifts, and Kolmogorov complexity of subshifts.
