论文标题
正装式的正装等于积极的热带硕士
The positive Dressian equals the positive tropical Grassmannian
论文作者
论文摘要
裙子和热带格拉曼尼亚参数化抽象和可实现的热带线性空间；但是总的来说，这位礼服比热带格拉斯曼尼亚人大得多。这两个空间都有自然的积极概念 - 正面的正装式和积极的热带格拉斯曼尼亚人（我们大约十五年前介绍了它） - 因此自然要问这两个积极的空间如何比较。在本文中，我们表明，正装式正装式等于热带硕士。使用Hypersimplex的正装式和常规上型肌张力细分之间的联系，我们利用结果为Da Silva的1987年猜想（由Ardila-Rincon-Williams在2017年首次证明）提供了新的“热带”证明，这些猜想是所有正向定向的Matroids均可取得了可观的。我们还表明，高血压的最优质的定期阳性细分由串联的矩阵多面体组成，并在Speyer的F-vector定理中达到平等。最后，我们举例说明了不规律的高刺阳性细分，并与热带超平面布置理论建立联系。
The Dressian and the tropical Grassmannian parameterize abstract and realizable tropical linear spaces; but in general, the Dressian is much larger than the tropical Grassmannian. There are natural positive notions of both of these spaces -- the positive Dressian, and the positive tropical Grassmannian (which we introduced roughly fifteen years ago) -- so it is natural to ask how these two positive spaces compare. In this paper we show that the positive Dressian equals the positive tropical Grassmannian. Using the connection between the positive Dressian and regular positroidal subdivisions of the hypersimplex, we use our result to give a new "tropical" proof of da Silva's 1987 conjecture (first proved in 2017 by Ardila-Rincon-Williams) that all positively oriented matroids are realizable. We also show that the finest regular positroidal subdivisions of the hypersimplex consist of series-parallel matroid polytopes, and achieve equality in Speyer's f-vector theorem. Finally we give an example of a positroidal subdivision of the hypersimplex which is not regular, and make a connection to the theory of tropical hyperplane arrangements.
