Obtaining the Chamanara Surface from the van der Corput sequence
Zawad Chowdhury, Francois Clement, Max Horwitz
我们研究了一个4个规则图家族,这些图形是为了测试在一系列不同实数中是否存在组合结构。 我们表明,由Kronecker序列构建的图形可以嵌入到环中,而由二进制van der Corput序列构建的图形可以嵌入到Chamanara表面,在这两种情况下都可以去除一个边缘。 这些结果暗示了序列图的一般理论,该理论可以嵌入到来自区间交换变换的特定翻译表面上。
We investigate a family of 4-regular graphs constructed to test for the presence of combinatorial structure in a sequence of distinct real numbers. We show that the graphs constructed from the Kronecker sequence can be embedded into the torus, while the graphs constructed from the binary van der Corput sequence can be embedded into the Chamanara surface, in both cases with the possible removal of one edge. These results allude to a general theory of sequence graphs which can be embedded into par...