Program
Enumerative Combinatorics and Applications 计数组合及应用
Student No.:50
Time:Wed/Fri 13:00-14:50, 2016-05-06~ 2016-06-01
Instructor:Guoniu Han  [National Center for Scientific Research, France]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2016-5-6
Ending Date:2016-6-1
 

Description:

This course is designed to show some methods and application in Enumerative Combinatorics. In contrast to traditional course on Combinatorics, I will focus on the bijective theory, a rising field of study since the last thirty years ; and show how to solve counting problems efficiently by discussing several examples. Its contain not only traditional counting problems for permutations, integer partitions and trees ; but also some modern research topics like symmetric functions, determinant evaluations, continued fractions and Young tableaux.

 

本课程介绍计数组合学的方法及应用。不同于传统的组合课程,这里重点介绍最近三十年来兴起的双射理论,并通过大量例子示范如何高效率地解决各种计数问题。其中既包括有关排列,整数的分拆,树等传统计数问题; 也涉及到对称函数,行列式,连分式,杨表等这样一些现在非常流行的研究课题.

 

 

Prerequisite:

 

Basic notions in linear algebra and mathematical analysis

 

线性代数,数学分析的基本知识

 

 

Reference:

 

[1] Nicholas Loehr, Bijective Combinatorics, CRC Press, 2011

 
[2] Stanley, Richard P., Enumerative Combinatorics, vol. 1,

Cambridge university press, 1997

 
[3] Stanley, Richard P., Enumerative Combinatorics, vol. 2,
Cambridge university press, 1999