SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1248-1260, January 2020.
The goal of this paper is to give a systematic method of constructing zero-free regions for the permanent in the sense of Alexander Barvinok, i.e., regions in the complex plane such that the permanent of a square matrix of any size with entries from this region is nonzero. We do so by refining the approach of Barvinok, which is based on his clever observation that a certain restriction on a set $S$ involving angles implies zero-freeness; we call sets satisfying this requirement angle-restricted. This allows us to reduce the question to a low-dimensional geometry problem (notably, independent of the size of the matrix!), which can then be solved more or less explicitly. We give a number of examples, improving some results of Barvinok.

中文翻译：

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永久角度限制集和零自由区

SIAM离散数学杂志，第34卷，第2期，第1248-1260页，2020年1月
。本文的目的是提供一种系统的方法，为亚历山大·巴维诺克（Alexander Barvinok）意义上的永久物构建零自由区，即区域在复平面中，使得具有来自该区域的条目的任何大小的方阵的永久性不为零。我们通过完善Barvinok的方法来做到这一点，Barvinok的方法是基于他的聪明观察，即对涉及角度的$ S $集的一定限制意味着零自由度。我们称满足该要求的集为角度受限。这使我们可以将问题简化为低维几何问题（特别是与矩阵的大小无关！），然后可以或多或少地明确解决该问题。我们举了一些例子，改进了Barvinok的一些结果。