ABSTRACT
In this chapter, we are going to introduce algorithms that count discrete mathematical objects using three operations: addition, subtraction and multiplication. The determinant and the Pfaffian of certain matrices will be the center of interest. The minors of Laplacians of graphs are the number of spanning trees or in case of directed matrices, the number of in-trees. The number of in-trees appears in counting the Eulerian circuits in directed Eulerian graphs. The Pfaffians of appropriately oriented adjacency matrices of planar graphs are the number of perfect matchings in those graphs.
