The investigator and his graduate research students study correlation and sorting problems for finite partially ordered sets and graphs. Specific goals of this research include (1) finding combinatorial arguments for correlation inequalities with attention to error estimates and structural information, (2) bijective proofs of log-concavity results and proportional transitivity problems, (3) continued investigation of balancing pairs and the cross product conjecture, and (4) understanding the boundary effects and the distinction between finite and infinite posets in correlation and sorting problems.
A major fraction of all scientific and business computing deals with the issue of sorting. Data must be aggregated according to some specified order, such as an alphabetical listing or a listing according to social security numbers. Updating records, locating files, and understanding the interplay between events which influence the speed at which files can be manipulated are fundamentally important research topics where advances will have immediate impact on a broad range of applications in business, industry and government. The investigator and his students are studying both the theoretical basis for research involving correlation and sorting and the practical implementation of algorithms derived from this research.
