Wei对偶定理的推广
Generalizations of Wei's Duality Theorem
摘要：
魏的著名对偶定理在几个方面得到推广，表示为除环上线性码的对偶定理，更一般地，表示为拟阵的对偶定理。这些结果被进一步推广，导致两个Wei型对偶定理的新的组合结构被引入和命名为{ \em的\em-拟阵}。这些拟阵推广了拟阵，是描述魏氏对偶定理中对偶性的合适的组合对象。对偶定理的一个新的证明，从而给出解释定理的组合术语。也给出了一般对偶定理的特殊情况，包括图中圈和键的对偶定理以及断面的对偶定理。
英文摘要：
Wei's celebrated Duality Theorem is generalized in several ways, expressed as duality theorems for linear codes over division rings and, more generally, duality theorems for matroids. These results are further generalized, resulting in two Wei-type duality theorems for new combinatorial structures that are introduced and named {\em demi-matroids}. These generalize matroids and are the appropriate combinatorial objects for describing the duality in Wei's Duality Theorem. A new proof of the Duality Theorem is thereby given that explains the theorem in combinatorial terms. Special cases of the general duality theorems are also given, including duality theorems for cycles and bonds in graphs and for transversals.
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