Replacing Pfaffians and applications
Abstract
Description
We present some Pfaffian identities, which are completely different from the Plücker relations. As consequences we obtain a quadratic identity for the number of perfect matchings of plane graphs, which has a simpler form than the formula by Yan et al (Graphical condensation of plane graphs: a combinatorial approach, Theoret. Comput. Sci., to appear), and we also obtain some new determinant identities.
22 pages, 2 figures
22 pages, 2 figures