Abstract Consider a hypergraph n d where the vertices are points of the d -dimensional cube [ n ] d and the edges are all sets of n points such that they are in one line. We study the structure of the group of automorphisms of n d , i.e., permutations of points of [ n ] d preserving the edges. In this paper we provide a complete characterization. Moreover, we consider the Colored Cube Isomorphism problem of deciding whether for two colorings of the vertices of n d there exists an automorphism of n d preserving the colors. We show that this problem is GI -complete. 3

中文翻译：

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立方体 nd 的自同构

摘要 考虑一个超图 nd，其中顶点是 d 维立方体 [ n ] d 的点，边都是 n 个点的集合，使得它们在一条线上。我们研究 nd 的自同构群的结构，即 [ n ] d 点的置换保留边缘。在本文中，我们提供了完整的表征。此外，我们考虑彩色立方体同构问题，该问题决定对于 nd 顶点的两种着色是否存在 nd 保留颜色的自同构。我们证明这个问题是 GI 完全的。3