博苏克-乌拉姆定理的选择结构推广
Selection-structure generalizations of the Borsuk-Ulam theorem
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中文总结 AI 辅助
研究博苏克-乌拉姆定理的选择结构推广，受弗里克和韦尔纳工作启发，证明相关类似物及沃洛维科夫定理版本，还给出公平划分应用，如火腿三明治和项链分割定理的选择结构版本。
中文摘要 AI 辅助
我们证明了由选择结构支配的博苏克-乌拉姆型结果。选择结构扩展了离散几何中彩色定理的拟阵框架，包括非拟阵的例子，如棋盘复形。受弗里克和韦尔纳对范定理及其彩色变体的拉东型强化的启发，我们证明了结论由拉东划分决定的选择结构类似物。我们还证明了由特弗伯格划分支配的沃洛维科夫定理的素幂选择结构覆盖版本。我们给出了公平划分的应用，包括火腿三明治和项链分割定理的选择结构版本。
英文摘要
We prove Borsuk-Ulam-type results governed by selection structures. Selection structures extend the matroidal framework for colorful theorems in discrete geometry and include non-matroidal examples such as chessboard complexes. Motivated by Frick and Wellner's Radon-type strengthening of Fan's theorem and its colorful variants, we prove selection-structure analogues whose conclusions are determined by Radon partitions. We also prove a prime-power selection-structure covering version of Volovikov's theorem, governed by Tverberg partitions. We include applications to fair partitions, including selection-structure versions of the ham sandwich and necklace splitting theorems.
