超立方体边界壳型的Gray码
A Gray Code for the Shelling Types of the Boundary of a Hypercube
摘要：
我们认为超立方体边界的两个壳是等价的，如果一个壳可以通过立方体的等距变换成另一个壳。我们观察到，一类不可分解的排列，双射等价于标准的双现字，可以用来编码一个代表从每个等价类的壳的边界的超立方体。因此，这些排列编码的超立方体的边界的脱壳类型。我们为这类置换构造了一个相邻转置格雷码。我们的结果是一个有符号的变种国王的结果表明，有一个换位格雷码不可分解的排列。
英文摘要：
We consider two shellings of the boundary of the hypercube equivalent if one can be transformed into the other by an isometry of the cube. We observe that a class of indecomposable permutations, bijectively equivalent to standard double occurrence words, may be used to encode one representative from each equivalence class of the shellings of the boundary of the hypercube. These permutations thus encode the shelling types of the boundary of the hypercube. We construct an adjacent transposition Gray code for this class of permutations. Our result is a signed variant of King's result showing that there is a transposition Gray code for indecomposable permutations.
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