论文标题
替代空间中的许多有限的位移不相等
Continuously many bounded displacement non-equivalences in substitution tiling spaces
论文作者
论文摘要
我们考虑在r^d中引起的替代瓷砖，这些替代位置与晶格相当并研究BD（x）的基数相当，这是相应的瓷砖空间x中的一组不同的BD类代表。我们证明了足够的条件，在此范围内，瓷砖空间持续不断地包含许多不同的BD类别和这样的平面。特别是，我们首次在这里表明这种基数可能大于一个。
We consider substitution tilings in R^d that give rise to point sets that are not bounded displacement (BD) equivalent to a lattice and study the cardinality of BD(X), the set of distinct BD class representatives in the corresponding tiling space X. We prove a sufficient condition under which the tiling space contains continuously many distinct BD classes and present such an example in the plane. In particular, we show here for the first time that this cardinality can be greater than one.
