极小半空间与热带多面体的外表示
Minimal half-spaces and external representation of tropical polyhedra
摘要：
本文给出了包含给定热带多面体的极小热带半空间的一个特征，并由此导出了一个反例，证明了极小热带半空间的个数可以是无穷多，从而反驳了热带文献中的一些说法，并反驳了F. Block和J. Yu.我们还建立了一个类似的闵可夫斯基-外尔定理，表明热带多面体可以等价地表示内部（在极值点和射线）或外部（在包含它的半空间）。多面体的一个规范的外部表示原来是由其热带极的极端元素提供的。我们描述这些极端的元素，特别显示，它们是由支持向量。
英文摘要：
We give a characterization of the minimal tropical half-spaces containing a given tropical polyhedron, from which we derive a counter example showing that the number of such minimal half-spaces can be infinite, contradicting some statements which appeared in the tropical literature, and disproving a conjecture of F. Block and J. Yu. We also establish an analogue of the Minkowski-Weyl theorem, showing that a tropical polyhedron can be equivalently represented internally (in terms of extreme points and rays) or externally (in terms of half-spaces containing it). A canonical external representation of a polyhedron turns out to be provided by the extreme elements of its tropical polar. We characterize these extreme elements, showing in particular that they are determined by support vectors.
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