Matchings and pfaffians
โ Scribed by K.K. Nambiar
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 139 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0895-7177
No coin nor oath required. For personal study only.
โฆ Synopsis
Pfaffian of a skew symmetric matrix obtained from an undirected graph is used to enumerate the matchings in the graph.
๐ SIMILAR VOLUMES
For any complex number ฮฑ and any even-size skew-symmetric matrix B, we define a generalization pf ฮฑ (B) of the pfaffian pf(B) which we call the ฮฑ-pfaffian. The ฮฑ-pfaffian is a pfaffian analogue of the ฮฑ-determinant studied in [T. Shirai and Y. Takahashi, J. Funct. Anal. 205 (2003) 414-463] and [D. V
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-ลฝ . secting paths may often be expressed as a Pfaffian, while, on
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