U.S.-Polish Research on "Probabilistic Combinatorics"

小行星9406971 这个美国-波兰概率组合学联合合作研究由埃默里大学的Vojtech Rodl博士和德怀特达夫斯博士与波兹南亚当密茨凯维奇大学离散数学系研究所的Michal Karonski博士、Tomasz Luczak博士和Andrzej Rucinski博士共同进行。 本研究所解决的问题属于概率组合学。 它们要么处理随机结构的性质，要么期望通过概率方法来解决。 波兰的研究人员是随机图理论的专家，除了其自身的兴趣之外，还为解决许多难题提供了强大的工具。 具体而言，研究人员将研究：（1）随机结构的极值和拉姆齐类型属性;（2）一些极值和拉姆齐类型问题的概率方法;（3）随机图和超图中的匹配;（4）具有有界最大度的图过程中的相变;（5）保序映射的枚举。 这一拟议中的数学和计算机科学研究通过使美国和波兰的领先专家能够联合收割机互补人才并在共同感兴趣和能力强的领域汇集研究资源，实现了推进科学的计划目标。 ***

9406971 Rodl This U.S.-Polish Joint Cooperative Research in Probabilistic Combinatorics is between Drs. Vojtech Rodl and Dwight Duffus of Emory University and Drs. Michal Karonski, Tomasz Luczak, and Andrzej Rucinski of the Institute of the Department of Discrete Mathematics of Adam Mickiewicz University in Poznan. The problems addressed in this research belong to probabilistic combinatorics. They either deal with properties of random structures or are expected to be solved by probabilistic means. The Polish investigators are experts in the theory of random graphs, which, besides its own interest, provides powerful tools for solving many hard problems. Specifically, the researchers will examine: (1) extremal and Ramsey type properties of random structures; (2) probabilistic approach to some extremal and Ramsey-type problems; (3) matchings in random graphs and hypergraphs; (4) phase transition in graph processes with bounded maximum degree; and (5) enumeration of order preserving maps. This proposed research in mathematics and computer science fulfills the program objectives of advancing science by enabling leading experts in the U.S. and Poland to combine complementary talents and pool research resources in areas of strong mutual interest and competence. ***