Hall 妻妾定理与几何 von Neumann 猜想的可计算版本
逻辑
2025-12-09 v4 组合数学
群论
摘要
我们证明了 Hall 妻妾定理的一个可计算版本，其中匹配实现了一个具有受控圈长的一元函数。我们将其应用于非顺从可计算粗空间。作为结果，我们得到了几何 von Neumann 猜想的一个可计算版本。
引用
@article{arxiv.2105.06304,
title = {A computable version of Hall's Harem Theorem and Geometric von Neumann Conjecture},
author = {Karol Duda},
journal= {arXiv preprint arXiv:2105.06304},
year = {2025}
}
备注
There are many new corrections with respect to v1 - v3. Also new pictures are included. Now the paper has a helpful companion: arXiv:2511.20724. Roughly it is a part of the version v2 of the present paper. It contains a variant of Hall's harem theorem with controlled sizes of cycles, where all computability issues are ruled out. The corresponding proof is similar and slightly simpler