Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have been found, it seems that most of them remain undiscovered. Improved results have been obtained in recent works by using the properties from which they are derived instead of the inequalities themselves. We apply here this strategy to the classification of matroids according to their representations and to the search for bounds on secret sharing for matroid ports.

中文翻译：

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拟阵端口的公共信息、拟阵表示和秘密共享

线性信息和秩不等式，例如英格尔顿不等式，是信息论和拟阵理论中的有用工具。尽管已经发现了许多这样的不等式，但它们中的大多数似乎仍未被发现。通过使用导出它们的属性而不是不等式本身，在最近的工作中已经获得了改进的结果。我们在这里将此策略应用于根据其表示的拟阵分类以及寻找拟阵端口秘密共享的边界。