This mathematica notebook computes valence independent formulas for map generating functions. The algorithm is based on the string equations.

1. SolveOddString.nb

These python scripts directly compute map counts.

2. countingMapsV5.py
3. gMapRecurrence5.py
The algorith used in countingMapsV5.py is based directly on the definition of a map. That is, the program iterates through a set of Wick pairings; for each Wick pairing the program determines whether the corresponding ribbon graph is connected; the faces of each connected ribbon graph are counted, thus the genus can be calculated, and a map count is incremented. This algorithm has superexponential time compexity with respect to the number of edges, and thus is not practical for computing map counts with more than 10 edges. The purpose of countingMapsV5.py is to check that the program gMapRecurrence5.py produces correct output. This program uses an algorithm based on the string equations to determine map counts recursively.