论文标题
偏斜区的矩形
Matroids over Skew Tracts
论文作者
论文摘要
在区域上的矩形提供了一个代数框架，同时概括了由Baker和Bowler提出的矩形，定向的矩形和有价值的矩阵的概念。 Pendavingh部分将该理论扩展到偏斜的Hyperfields，并根据准plücker坐标提出了一个新的公理系统。我们提出了一种在偏斜区域上的成矩形理论，该理论概括了原始的原子状学理论，以及Pendavingh开发的偏斜高领域的弱矩阵理论。我们在电路，准plücker坐标和双对方面为此类矩阵提供了几个隐态公理系统。
Matroids over tracts provide an algebraic framework simultaneously generalizing the notions of matroids, oriented matroids, and valuated matroids, presented by Baker and Bowler. Pendavingh partially extended this theory to skew hyperfields and presented a new axiom system in terms of quasi-Plücker coordinates. We present a theory of matroids over skew tracts, which generalizes both the theory of matroids over tracts and the theory of weak matroids over skew hyperfields developed by Pendavingh. We give several cryptomorphic axiom systems for such matroids in terms of circuits, quasi-Plücker coordinates and dual pairs.
