MATHEMATICAL SCIENCES: Homology Representations Arising FormPosets of Partitions and Subspace Arrangements

小行星9400875 该奖项资助Sheila Sundaram教授在代数组合学方面的研究。 特别是孙达拉姆教授将分区格的subposets的同源性。 她将试图建立惠特尼同源模与某些偏序集实际上是置换模。 这一猜想的影响有关的正切和Genocchi数的细化。 这项研究福尔斯属于广义的组合学范畴， 这是当今数学中最活跃的领域之一。从根本上说，组合学是对系统计数和排列的研究。 当对象难以列出时，计数可能非常困难，组合学家寻找克服这些困难的通用方法。 今天的组合学利用了各种各样的最先进的和现代的数学技术。 虽然它的根源可以追溯到几个世纪，但在过去的几十年里，该领域取得了爆炸性的发展。 这一增长来自于其在 从现代技术的成功到计算的问题。 ***

9400875 Sundaram This award funds the research of Professor Sheila Sundaram in algebraic combinatorics. In particular Prof. Sundaram will the homology of subposets of the partition lattice. She will try to establish that Whitney homology modules associated to certain posets are in fact permutation modules. This conjecture has implications regarding refinements of the tangent and Genocchi numbers. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. At its roots, combinatorics is the study of systematic counting and arrangement. Counting can be incredibly difficult when the objects are difficult to list, and combinatorists look for general methods for overcoming these difficulties. Today's combinatorics makes use of a wide variety of the most advanced and modern mathematical techniques. Although its roots go back several centuries, the field has had an explosive development in the past few decades. This growth comes from its importance in communications and information technology and from the success of modern techniques to problems of counting. ***