报告题目:n-立方体的两个层级定义的图的控制数

TopicThe domination number of the graph defined by two levels of then-cube

报告人:匈牙利科学院Gyula Katona院士

Speaker:Prof.Gyula Katona,Academician of Hungarian Academy of Sciences

讲座时间:2018年10月10日(星期三)上午10:30-11:30

Time10:30am-11:30am,October10, 2018(Wednesday)

讲座地点:西北工业大学理学院应用数学系214会议室(长安校区)

PlaceConference Room 214,Department of Applied Mathematics,School of Natural and Applied Sciences

邀请人:张胜贵教授

HostProf. Shenggui Zhang

承办学院:西北工业大学理学院

Host college:School of Natural and Applied Sciences

联系人:刘晓刚

ContactXiaogang Liu

联系电话:13379232180

Phone:13379232180

报告简介

将n-元集合的所有k-元子集和s-元子集看成一个二部图的顶点,其中k>s,两个顶点相邻当且仅当s-元子集是对应的k-元子集的子集。令Gk,s表示此图。本报告将准确的给出Gk,1的控制数。我们也将给出Gk,2的控制数的上、下界的估计,并提出关于渐进性质的一个猜想。

Introduction

Consider allk-element subsets ands-element subsets (k>s) of ann-element set as vertices of a bipartite graph.Two vertices are adjacent if the correspondings-element set is a subset of the correspondingk-element set.LetGk,sdenote this graph. In this talk, the domination number of Gk,1 will exactly be determined. We also give lower and upper estimates on the domination number of Gk,2 and pose a conjecture of asymptotic nature.

报告人简介

Gyula Katona求学于匈牙利布达佩斯的罗兰大学,导师为Paul Erdős、Alfréd Rényi和Pál Turán。获得学位后,Gyula Katona主要任职于匈牙利科学院数学研究所(现为Rényi研究所),自1964年以来,他也在罗兰大学任教。他曾为8所美国大学的客座教授(共12个学期)。Gyula Katona教授的主要研究领域是极值集合理论,最著名的两个结果是影子定理(亦称为Kruskal-Katona定理)和使用循环置换证明了Erdős-Ko-Rado定理,后者被写进“Proofs from the Book”一书中(Aigner和Ziegler按照Paul Erdős的指示收集了很多漂亮的证明)。Gyula Katona教授已发表学术论文150多篇,内容涉及组合学以及组合学在概率论、数据库理论和密码学中的应用。他已有20余名学生,其中包括Zsolt Baranyai、Peter Frankl、Zoltán Füredi、Ervin Győri和László Pyber。Gyula Katona教授是匈牙利科学院的院士,并且他的3名学生也成为了匈牙利科学院的院士。Gyula Katona教授还是欧洲科学院的院士和保加利亚科学院的外籍院士。Gyula Katona教授曾担任Rényi研究所所长10年,担任秘书长9年,并担任匈牙利数学学会主席12年。Gyula Katona教授的两个儿子都从事数学研究,他的大儿子(名字与Gyula Katona教授只有中间名字不同)也从事组合数学研究,目前是布达佩斯理工大学数学系的系主任。他的小儿子目前是加州大学伯克利分校商学院的教授。

Speakers Biography

Gyula Katona studied in Budapest, Hungary at the Eötvös University. His masters were Paul Erdős, Alfréd Rényi and Pál Turán. After receiveing his diploma, his main employer was the Mathematical Institute of the Hungarian Academy of Sciences (now Rényi Institute),but he has been teaching at the Eötvös University also since 1964. He spent 12 semesters at 8 different American Universities as visiting professor. His main research area is Extremal Set Theory, and the best known results are the Shadow Theorem, called Kruskal-Katona theorem and the proof of the Erdős-Ko-Rado theorem using cyclic permutations. The latter one is included in the book "Proofs from the Book" in which Aigner and Ziegler collected the nice proofs following the instructions of Paul Erdős. His more than 150 publications include applications of Combinatorics in Probability Theory, Database Theory and Cryptology. He had more than 20 students, among others Zsolt Baranyai, Peter Frankl, Zoltán Füredi, Ervin Győri and László Pyber. He is a member of the Hungarian Academy of Sciences, but 3 of his former students also became members of the same.He is also a member of the European Academy of Sciences and a foreign member of the Bulgarian Academy of Sciences. He served 10 years as the director of the Rényi Institute, 9 years as the Secretary General and 12 years as the President of the Hungarian Mathematical Society.Both of his sons studied mathematics. The older one whose name differs only in the middle initial is also working in Combinatorics and is the head of one of the mathematical departments of the Technical University of Budapest. The younger son is a professor at the Business School of the University of California, Berkeley.

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