Extremal graphs, hereditary and random structures

PI和共同PI研究了L和L的性质如何影响各种组合结构的g L和L参数，这是所谓图兰数问题的一个非常一般的框架。PI和co-PI强调五个不同的方面：三元系的Turan数、遗传族的基数、自然产生Turan数的图的几何/代数表示。它们研究更一般的编码理论问题，研究随机组合结构，特别是各种Bootstrap渗漏模型的相变。组合学，换句话说，离散数学，研究有限但大的结构，其中许多起源于计算机科学。组合学是编码理论、计算机图形学、计算机科学、密码学和通信理论的理论基础。组合学家正在寻找经济、存储和搜索数据结构的快速而可靠的方法。各种各样的组合问题涉及L或L的性质，或者使用局部概率来确定(或估计)全局参数来描述更大的图景。这种局部性质对全局参数的影响是本建议的主题。

The PI and the co-PI study how l o c a l properties affect the g l o b a l parameters of various combinatorial structures.This is a very general framework of the so-called Turan number problems. The PI and the co-PI emphasize five different aspects:Turan numbers of triple systems, cardinalities of hereditary families,geometrical/algebraic representations of graphs where Turan numbers naturally emerge, they study more general coding theory problems, and investigate random combinatorial structures, especially the phase transition of various models of bootstrappercolation.Combinatorics, in other words Discrete Mathematics, studies finite, but large structures, many of them arising from computer science.Combinatorics is the theoretical basis of coding theory, computergraphics,computer science, cryptography and communication theory.Combinatorists are looking for economical, fast and reliable ways tostore and search data structures.A wide variety of combinatorial problems deal with l o c a l properties, or use local probabilities in order to determine (or estimate) global parameters to describe the bigger picture.This effect of local properties on global parameters is the subject of this proposal.