高度对称的不稳定 maniplexes
Highly symmetric unstable maniplexes
AI总结：
本文研究了不稳定 maniplexes 的最大对称度问题，证明了对于 rank n > 2，存在 2-orbit maniplexes。
摘要：
一个 rank n 的 maniplex 是一个 n-度的正确边着色图，它同时推广了表面上的映射和抽象多面体。在 maniplexes 中的稳定性问题是图的稳定性问题的自然变种。如果 maniplex 的 canonical double cover 的每一个 automorphism 都是原 maniplex 的某个 automorphism 的提升，则该 maniplex 是稳定的。由于其非常丰富的结构，regular（最大对称）maniplexes 始终是稳定的。因此，自然地要问，一个不稳定 maniplex 可以承受的最大可能对称度是多少。在 maniplexes 中的对称性通常通过其 automorphism 组对旗帜（节点）的轨道数来衡量。已知对于 rank 3，有一些具有 4 个旗帜轨道的不稳定 maniplexes 的家族。在本文中，我们证明了对于每个 rank n > 2，2-orbit maniplexes 都存在。
英文摘要：
A maniplex of rank n s an n-valent properly edge-coloured graph that generalises, simultaneously, maps on surfaces and abstract polytopes. The problem of stability in maniplexes is a natural variant of the problem of stability in graphs. A maniplex is stable if every automorphism of its canonical double cover is a lift of some automorphism of the original maniplex. Due to their very rich structure, regular (maximally symmetric) maniplexes are always stable. It is thus natural to ask what is the maximum possible degree of symmetry that a maniplex that is not stable can admit. Symmetry in maniplexes is usually measured by the number of orbits on flags (nodes) of their automorphism group. A few families of unstable maniplexes with 4 flag-orbits are known for rank 3. In this paper, we show that 2-orbit maniplexes exist for every rank n > 2$.
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。
