✦ LIBER ✦

Nonintersecting Paths, Pfaffians, and ▵-Matroids

✍ Scribed by Myriam Desainte-Catherine; Walter Wenzel

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 256 KB
Volume: 19
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.1997.0554

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we study ^-matroids induced by nonintersecting paths in a directed graph. The association between nonintersecting paths and ^-matroids is derived from Pfaffians. On the one hand, certain numbers of k-tuples of noninter-Ž . secting paths may often be expressed as a Pfaffian, while, on the other hand, representability problems for ^-matroids may be studied in terms of Pfaffians. It is shown that ^-matroids induced by nonintersecting paths are representable over fields of any characteristic and that weightings defined on the edge set and with values in some linearly ordered abelian group give rise to valuated ^-matroids.

📜 SIMILAR VOLUMES

Pfaffian forms and Δ-matroids

✍ Walter Wenzel 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 794 KB

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}