ENUMERATION OF POLYENE HYDROCARBONS - A COMPLETE MATHEMATICAL SOLUTION

Polyenoid systems (or polyenoids) are trees which can be embedded in a hexagonal lattice and represent CnHn+2 polyene hydrocarbons. Complete mathematical solutions in terms of summations and in terms of a gener ating function are deduced for the numbers of polyenoids when overlapp ing edges and/or vertices are allowed. Geometrically planar polyenoids (without overlapping vertices) are enumerated by computer programming . Thus the numbers of geometrically nonplanar polyenoids become access ible. Some of their numbers are confirmed by combinatorial constructio ns, a pen-and-paper method.