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Pfaffian forms and Δ-matroids

✍ Scribed by Walter Wenzel

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
794 KB
Volume
115
Category
Article
ISSN
0012-365X

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✦ Synopsis

Wenzel, W., Pfaffian forms and d-matroids, Discrete Mathematics 115 (1993) 253-266.

In this paper it is shown that skew-symmetric n x 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 '@({l, . . . . n}), which satisfy certain identities. As an application, we describe representability of d-matroids by skew-symmetric matrices in terms of these maps. This suggests a definition of orientable and valuated d-matroids or, more generally, of d-matroids with coefficients which is analogous to the corresponding concept studied in matroid theory.

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