Sauer Problems for Set Systems

小行星9401351 该奖项资助安德鲁·拉德克利夫教授对绍尔定理及其影响的研究。 拉德克利夫教授打算研究反链的痕迹，一般的痕迹问题和反链。 这项工作应该有影响的学习理论，经验的过程和理论的Banach空间。 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的研究，尽管这项研究更多地涉及比较计数结果。 绍尔定理是一个一般不等式，它允许人们知道一个集合包含的对象比另一个集合多。 当然，集合必须是特定类型的，但条件并不难满足。虽然它的根源可以追溯到几个世纪，但组合学领域在过去几十年中有了爆炸性的发展。 这种增长来自于它在通信和信息技术中的重要性，以及在这项工作中，人工智能。

9401351 Radcliffe This award funds the research of Professor Andrew Radcliffe into Sauer's theorem and its implications. Prof. Radcliffe intends studying traces of antichains, general trace problems and antichains. The work should have implications for learning theory, empirical processes and the theory of Banach spaces. 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, although this research is more involved with comparing the results of counting. Sauer's theorem is a general inequality that allows one to know that one collection contains more objects than another. Of course the collections must be of particular types, but the conditions are not hard to satisfy. Although its roots go back several centuries, the field of combinatorics has had an explosive development in the past few decades. This growth comes from its importance in communications and information technology, and as in this work, artificial intelligence.