重新审视圆柱体上的硬正方形
Hard squares on cylinders revisited
摘要：
我们考虑了圆柱边界条件下正方形网格的独立复形。当其中一个维度是小的，我们使用简单的减少引起的边缘删除，以显示明确的自然同伦等价这些空间之间。第二部分推广了Jonsson关于奇周长圆柱的欧拉示性数的计算结果。我们描述了一系列的结果，甚至周长的圆柱。最后，我们定义了一个完全独立的组合模型（项链），计算圆柱网格的欧拉示性数的生成函数。我们推测这个模型有一些特别简单的结构。
英文摘要：
We consider the independence complexes of square grids with cylindrical boundary conditions. When one of the dimensions is small we use simple reductions induced by edge removals to show explicit natural homotopy equivalences between those spaces. In the second part we expand the results of Jonsson, who calculated the Euler characteristic of cylinders with odd circumference. We describe a series of results for cylinders of even circumference. Finally we define a completely independent combinatorial model (necklaces) which calculates the generating functions of the Euler characteristic of cylindrical grids. We conjecture that this model has some particularly simple structure.
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。
