以 K₁₀ 为缩影的图式流形的同胚分类的一个下界

A Lower Bound for the Homeomorphic Classi?cation of Graphlike Manifolds Retracted to K₁₀

摘要: 本文根据伴随矩阵的积和式以及特征多项式这两个拓扑不变量进行计算，在原先已有的算法上进 行一定的改进，结合 Ryser 算法提高了一定的计算效率，探讨了以 K₁₀ 为一维骨架的缩影的图 式流形同胚分类的一个下界，最后得出结论，根据特征多项式的不同个数得到 K₁₀ 图式流形至少 有 32314 个同胚类，再结合积和式，可以得到 K₁₀ 图式流形至少有 37300 个同胚类。

Abstract: This paper performs calculations based on two topological invariants, namely the permanent and the characteristic polynomial of the associated matrix. It implements certain improvements on the existing algorithms, and combines them with the Ryser algorithm to enhance computational efficiency to a certain extent. The paper also explores a lower bound for the homeomorphic classification of graphlike manifolds whose 1-skeletons are K₁₀. Finally, it draws the following conclusions: based on the number of distinct characteristic polynomials, the K₁₀ graphlike manifolds have at least 32,314 homeomorphism classes; further combined with the permanent, it can be concluded that the K₁₀ graphlike manifolds have at least 37,300 homeomorphism classes.