An exploration of the permanent-determinant method

Details An exploration of the permanent-determinant method An exploration of the permanent-determinant method

1998-10-14

arxiv.org/abs/math/9810091v2

Electron. J. Combin. 5 (1998), #R46

Mathematics

Combinatorics

16 pages, 20 in-line figures. This version has some minor clarifications suggested by the referee

Scientific paper

The permanent-determinant method and its generalization, the Hafnian-Pfaffian method, are methods to enumerate perfect matchings of plane graphs that was discovered by P. W. Kasteleyn. We present several new techniques and arguments related to the permanent-determinant with consequences in enumerative combinatorics. Here are some of the results that follow from these techniques: 1. If a bipartite graph on the sphere with 4n vertices is invariant under the antipodal map, the number of matchings is the square of the number of matchings of the quotient graph. 2. The number of matchings of the edge graph of a graph with vertices of degree at most 3 is a power of 2. 3. The three Carlitz matrices whose determinants count a x b x c plane partitions all have the same cokernel. 4. Two symmetry classes of plane partitions can be enumerated with almost no calculation.

Affiliated with

Also associated with

No associations

Rating

An exploration of the permanent-determinant method does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An exploration of the permanent-determinant method, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An exploration of the permanent-determinant method will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-107168