This research is in the area of combinatorics. Specifically problems in enumerative combinatorics, including symmetric functions and their generalizations, the theory of P- recursiveness, lattice path enumeration, permutation enumeration, and hypergeometric series will be studied. This research covers a broad front in combinatorics, the mathematics associated with combinations of finite sets. Much attention will be spent in various "counting problems", one of the most important and difficult areas of combinatorics. Moreover the potential applications to other areas such as computer science are very important. Thus this research holds much promise for excellent contributions.
