Planar Rosa：一类具有 $2n$ 阶旋转对称性的准周期替换离散平面平铺
Planar Rosa : a family of quasiperiodic substitution discrete plane tilings with $2n$-fold rotational symmetry
AI总结：
提出 Planar Rosa 替换平铺族，证明其具有 $2n$ 阶旋转对称性且满足离散平面条件，并指出 Sub Rosa 平铺不满足该条件，完善了奇偶 $n$ 的结果。
摘要：
我们提出了 Planar Rosa，这是一类具有 $2n$ 阶旋转对称性的菱形平铺，由原始替换生成，且也是离散平面平铺，即通过高维离散平面的投影获得。离散平面条件是切割与投影条件的放松版本。我们还证明了 Kari 和 Rissanen 定义的具有 $2n$ 阶旋转对称性的 Sub Rosa 替换平铺甚至不满足较弱的离散平面条件。我们针对所有偶数 $n\geq 4$ 证明了这些结果。这完善了我们之前发表的关于奇数 $n$ 的结果。
英文摘要：
We present Planar Rosa, a family of rhombus tilings with a $2n$-fold rotational symmetry that are generated by a primitive substitution and that are also discrete plane tilings, meaning that they are obtained as a projection of a higher dimensional discrete plane. The discrete plane condition is a relaxed version of the cut-and-project condition. We also prove that the Sub Rosa substitution tilings with $2n$-fold rotational symmetry defined by Kari and Rissanen do not satisfy even the weaker discrete plane condition. We prove these results for all even $n\geq 4$. This completes our previously published results for odd values of $n$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
