Pfaffian forms and Delta-matroids
Pfaffian forms and Delta-matroids
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普法夫形式和 Delta 拟阵
DOI：
10.1016/0012-365x(93)90494-e
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
W. Wenzel
中科院分区：
文献类型：
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作者：
W. Wenzel
本文证明了域K中系数的反对称n× n-矩阵通过Pfweian形式与定义在幂集B（{1，...，n}）上的K-值映射一一对应，并满足一定的恒等式.作为应用，我们利用这些映射描述了Δ-拟阵的反对称矩阵表示.这就提出了可定向和赋值的Δ-拟阵的定义，或者更一般地说，具有系数的Δ-拟阵的定义类似于拟阵理论中研究的相应概念。
In this paper it is shown that skew-symmetric n× n-matrices with coefficients in a field K correspond via Pfaffian forms in a canonical one-to-one fashion to K-valued maps defined on the power set B ({1,…, n}), which satisfy certain identities. As an application, we describe representability of Δ-matroids by skew-symmetric matrices in terms of these maps. This suggests a definition of orientable and valuated Δ-matroids or, more generally, of Δ-matroids with coefficients which is analogous to the corresponding concept studied in matroid theory.