Correlation and Sorting

调查员和他的研究生研究有限偏序集和图的相关性和排序问题。 本研究的具体目标包括：（1）寻找相关不等式的组合参数，并注意误差估计和结构信息，（2）对数正态结果和比例传递性问题的双射证明，（3）继续研究平衡对和叉积猜想，以及（4）理解边界效应以及相关和排序问题中有限和无限偏序集之间的区别。所有科学和商业计算的主要部分都涉及分类 数据必须按照某种特定的顺序进行汇总，例如按字母顺序排列或按社会安全号码排列。 更新记录、定位文件以及了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。 调查员和他的学生正在研究的理论基础，研究涉及相关性和排序和实际执行的算法，从这项研究。

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.