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2014年组合与图论研讨会

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2014年厦门组合与图论研讨会于3月20日-23日在厦门大学数学科学学院举行。本次研讨会由南开大学组合数学中心倡议、由厦门大学数学科学学院主办,来自南开大学,南京大学,山东大学,太原理工大学、华中师范大学,青海师范大学,洛阳师范学院和澳大利亚newcastle大学、以及集美大学和厦门理工学院等高校老师和研究生70余人参加了研讨会。

3月21日上午8:30时,开幕式在海韵园实验楼105报告厅举行。数学科学学院数学与应用数学系主任金贤安教授主持了开幕式。国家教学名师、厦门大学数学科学学院院长林亚南教授代表学院致辞,欢迎各位专家的到来,介绍了学院和厦门地区组合图论研究团队的情况、预祝会议圆满成功,并感谢各位专家长期以来对我院组合图论团队的关心和支持。国际数学化学科学院院士、厦门大学张福基教授和国际数学化学科学院院士、南开大学李学良教授分别致辞。开幕式后,部分参会师生一起合影留念。

 

(部分与会师生合影)

3月21日上午和下午,研讨会安排了2场45分钟报告和6场30分钟报告,45分钟报告分别为国家自然科学杰出青年基金获得者、南京大学孙智伟教授的题为《Problems on Combinatorial Properties of Primes》的报告和南开大学组合数学中心高维东教授的题为《On the EGZ-constant and short zero sum sequences》的报告。30分钟报告分别为:钱建国教授的题为《Enumeration of unlabeled uniform hypergraphs and directed hypergraphs》、候庆虎教授的题为《扩展的Zeilberger算法及其应用》、李书超教授的题为《Independent sets, independence polynomials and maximal independent sets of graphs》、陈海燕教授的题为《Some results on the Abelian sandpile model》、王光辉副教授的题为《Neighbor sum distinguishing colorings of graphs》和王星炜副教授的题为《Analytical properties of combinatorial sequences》的报告。3月22日上午,李学良教授还为我院“拔尖班”学生作了题为《谈谈图论》的魅力数学讲座。

 

此次研讨会的主要目的在于加强我院组合图论研究团队教师与兄弟院校组合图论专家的学术交流、扩大我院组合图论研究团队研究生的学术视野和我院组合图论研究团队在全国的影响力。研讨会达到了预期目的。

 

 

2014年组合与图论研讨会

2014年3月21日,星期五,海韵实验楼105报告厅

 

时间

主持人

报告人

08:30-09:00

开幕式

09:00-09:45

张福基教授

孙智伟教授 (南京大学)

09:45-10:30

高维东教授 (南开大学)

10:30-11:00

11:00-11:30

郭晓峰教授

钱建国教授 (厦门大学)

11:30-12:00

侯庆虎教授 (南开大学)

12:15

15:00-15:30

张莲珠教授

李书超教授 (华中师大)

15:30-16:00

陈海燕教授 (集美大学)

16:00-16:30

16:30-17:00

晏卫根教授

王光辉副教授  (山东大学)

17:00-17:30

王星炜副教授 (南开大学)

18:00

 

学术报告题目与摘要

 

1. 报告人:孙智伟,南京大学数学系

题目:Problems on Combinatorial Properties of Primes

摘要:For let (x) be the number of primes not exceeding x. The asymptotic behaviors of the prime-counting function (x) and the n-th prime pn  have been studied intensively in analytic number theory. Surprisingly, we find that (x) and pn have many combinatorial properties which should not be ignored. In this talk we will introduce many new open problems on combinatorial properties of primes as well as some connections between primes and partition functions.

 

2. 报告人:高维东,南开大学组合数学中心

题目:On the EGZ-constant and short zerosum  sequences

摘要:Let G be a finite additively written abelian group with exponent exp(G)=m. We call a sequence S of elements from G a zero-sum sequence if the sum of all terms of S equals to zero, the identity element of G. We shall discuss some problems and present some new results on zero-sum subsequences of length between 1 and m.  

 

3. 报告人:钱建国,厦门大学数学科学学院

题目:Enumeration of unlabeled uniform hypergraphs and directed hypergraphs

摘要:We consider the enumeration of unlabeled uniform hypergraphs and directed hypergraphs by using Polya's counting theory and Burnside's counting lemma. Instead of characterizing the cycle index of the permutation group acting on the hyperedge setε, we treat each cycle in the disjoint cycle decomposition of a permutation ρacting onεas an equivalence class (or orbit) ofεunder the operation of the group generated by ρ. Compared to the cycle index-based method, our method is more effective in dealing with the enumeration of hypergraphs. Using this method we establish an explicit counting formula of the unlabeled k-uniform hypergraphs and directed hypergraphs for any integer k with 1≤k≤n, where n is the order of the hypergraphs.  Based on our counting formula, the asymptotic behaviour for the number of these two types of graphs are also analyzed.

 

 

4. 报告人:侯庆虎,南开大学组合数学中心

题目:扩展的Zeilberger算法及其应用

摘要:我们将简介扩展的Zeilberger算法的理论和算法,并以正交多项式计算、q级数等式推导、Bernoulli数等式证明为例,展示该算法的应用。

 

 

 

5. 报告人:李书超,华中师范大学数学与统计学学院

题目:Independent sets, independence polynomials and maximal independent sets of graphs

摘要: In this talk, we survey some results on independent sets, independence polynomials and maximal independent sets of graphs. In particular, we determined the largest number of maximal independent sets among all n-vertex bipartite graphs with at least one cycle. The corresponding external graphs are characterized.

 

6. 报告人:陈海燕,集美大学理学院

题目:Some results on the Abelian sandpile model

摘要: Let G be a connected graph with a distinguished vertex . The Abelian sandpile model is a Markoc chain on G. The recurrent states of this chain are main concerns of researchers. It has been found that the recurrent set has rich algebraic and combinatoric  structures, such as it has a finite abelian group structure( called the critical group) with order equal to the tree-number of G.  In this report, we simply introduce some our recent work about the height distribution function and the critical group of the recurrent states.

 

7. 报告人:王光辉,山东大学数学学院

题目:Neighbor sum distinguishing colorings of graphs

摘要: Colorings and labellings related to sums of the colors have been studied widely. The family of such problems
 includes e.g. vertex-coloring [k]-edge-weightings, total weight choosability, magic and antimagic labellings and the
irregulaity strength. Among them there are the 1-2-3 Conjecture due to Karo'nski, Luczak and Thomasson  and 1-2
Conjecture due to Przybylo and Wo'zniak. In a proer edge (total) coloring of G, let f(v) denote the total sum of colors
around v. If for each edge uv, f(u)≠f(v), we call such edge (total) coloring a {\it neighbor sum distinguishing coloring}.
We will give some results about neighbor sum distinguishing colorings.
 

8. 报告人:王星炜,南开大学组合数学中心

题目:Analytical properties of combinatorial sequences

摘要:Log-concave and log-convex sequences often arise in combinatorics, algebra, analysis and geometry, as well as in probability and statistics. By establishing the connection between continued functions and combinatorial sequences, we prove that some combinatorial sequences propose analytical properties, including log-convexity, ratio log-convexity, infinitely log-monotonicity, Turan inequality.