A semantic tree algorithm for the generation of sextet polynomials of hexagonal systems

The sextet polynomial that counts different ways of selecting varying number of resonating sextets on the hexagonal system is computed using a search based symbol manipulation algorithm. This is a #P Complete combinatorial enumeration problem, and artificial intelligence (AI) is employed for efficient enumeration. This is done by selective exploration of the semantic tree defined for that purpose. Hexagons of the graph are defined as symbols and each node of the tree is defined as a set of mutually disjoint hexagon patterns of the graph. The sextet polynomial is generated by enumerating a suitable subset of the nodes of the tree. A pruning heuristic that avoids redundant branches by a priori learning at selected intelligent branches of the semantic tree is designed.