Manin and Schechtman introduced a family of arrangements of hyperplanes generalizing classical braid arrangements, which they called the discriminantal arrangements. Athanasiadis proved a conjecture by Bayer and Brandt providing a full description of the combinatorics of discriminantal arrangements in the case of very generic arrangements. Libgober and Settepanella described a sufficient geometric condition for given arrangements to be non-very generic in terms of the notion of dependency for a certain arrangement. Settepanella and the author generalized the notion of dependency introducing r-sets and \(K_{\mathbb {T}}\)-vector sets, and provided a sufficient condition for non-very genericity but still not convenient to verify by hand. In this paper, we give a classification of the r-sets, and a more explicit and tractable condition for non-very genericity.

Manin 和 Schechtman 引入了一系列超平面排列，概括了经典辫子排列，他们称之为判别排列。Athanasiadis 证明了 Bayer 和 Brandt 的猜想，提供了在非常一般的安排情况下判别安排的组合学的完整描述。Libgober 和 Settepanella 描述了给定排列的充分几何条件，根据特定排列的依赖性概念，该排列不是非常通用。Settepanella 和作者概括了依赖关系的概念，引入了r -sets 和\(K_{\mathbb {T}}\)-vector sets，为非通用性提供了充分条件，但仍然不方便手工验证。在本文中，我们给出了r集的分类，以及非非常通用的更明确和易于处理的条件。