Correlation and Sorting

研究者和他的研究生研究有限偏序集和图的相关和排序问题。本研究的具体目标包括：(1)在考虑误差估计和结构信息的情况下，寻找相关不等式的组合论证；(2)对数凹性结果和比例传递性问题的双客观证明；(3)继续研究平衡对和叉积猜想；(4)理解相关和排序问题中的边界效应以及有限和无限偏集之间的区别。所有科学和商业计算的主要部分都涉及排序问题。数据必须按照某些指定的顺序聚合，例如按字母顺序排列的列表或按社会安全号码排列的列表。更新记录、定位文件和理解影响文件操作速度的事件之间的相互作用是非常重要的研究课题，其进展将对商业、工业和政府的广泛应用产生直接影响。研究者和他的学生正在研究相关和排序研究的理论基础，以及从这项研究中得出的算法的实际实施。

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.