Addition-deletion theorem for free hyperplane arrangements and combinatorics
Addition-deletion theorem for free hyperplane arrangements and combinatorics
复制标题
自由超平面排列和组合学的加减定理
DOI：
10.1016/j.jalgebra.2022.06.028
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发表时间：
2022
影响因子：
0.9
通讯作者：
Takuro Abe
中科院分区：
文献类型：
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作者：
Takuro Abe
在超平面排列理论中，最重要也是最困难的问题是几个性质的组合依赖性。在这篇文章中，我们证明了寺尾的著名的自由安排的加法定理是组合的。结合这些天来的其他发展，我们可以证明所有的添加-删除框架是组合的。作为推论，我们可以定义一类新的自由排列，称为超平面的加性自由排列，它可以通过仅使用加法定理从空排列构造。这样我们就可以证明寺尾猜想在这一类中是正确的。作为应用，我们证明了所有理想-Shi安排的自由度是组合的。
In the theory of hyperplane arrangements, the most important and difficult problem is the combinatorial dependency of several properties. In this article, we prove that Terao's celebrated addition theorem for free arrangements is combinatorial. Combining other developments in these days, we can show that all the addition-deletion framework is combinatorial. As a corollary, we can define a new class of free arrangements called the additively free arrangement of hyperplanes, which can be constructed from the empty arrangement by using only the addition theorem. Then we can show that Terao's conjecture is true in this class. As an application, we prove that the freeness of all ideal-Shi arrangements is combinatorial.