离散数学短课程招生简章

国家天元数学东南中心拟于2026年5月18日至5月28日开设离散数学短课程，相关安排如下：

一、短课程介绍

Course 1： Graph Polynomials

Abstract: This short course will introduce several classical graph polynomials, including the Tutte polynomial, chromatic polynomial, flow polynomial, independence polynomial, characteristic polynomial, etc. It is hoped that the course will inspire and encourage more young researchers to engage in these areas. The course will cover fundamental concepts, key properties, established results, open problems, and recent developments related to these graph polynomials.

Tentative Contents:

1. Tutte polynomial (3 hours);

2. Chromatic polynomial (3 hours);

3. Flow polynomial (2 hours);

4. Tau-polynomial (1 hour);

5. DP-color functions (1 hour);

6. Stanley’s chromatic symmetric function (2 hours);

7. Independence polynomial (2 hours);

8. Characteristic polynomial (1 hour).

Course 2： An introduction to matroids

Abstract: As a short introduction course for matroid theory, it will bring in the basic axiom systems such as matroid axioms of independent sets, bases, circuits, rank functions and closure operators. Matroid restrictions, contractions, matroid minors and duality, as well as other common matroid operations will also be discussed. Selected topics include matroid connectivity, regular and binary matroids, Seymour’s decomposition theorem with applications.

Tentative Contents:

1. Basic matroid axiom systems (4 hours);

2. Common matroid operations and matroid minors (2 hours);

3. Common matroid families and matroid duality (3 hours);

4. Connectivity and regular matroid decompositions (3 hour);

5. Applications of Seymour’s Decompositions (3 hour).

二、课程日期安排

2026年5月18日报到，5月19日-27日上课，5月28日离会。

三、短课程地点

1. 上课地点：厦门大学海韵园实验楼S103、S105

2. 住宿地点：鹭江佲家酒店，福建省厦门市思明区曾厝垵龙虎山路382号，0592-2199099（国家天元数学东南中心为厦门市外学员提供住宿，标间，两人一间）

3. 用餐地点：海韵食堂

四、招生对象

优秀青年教师、博士生、硕士生、高年级本科生（招生人数30人）

五、联系人

马老师（tymath3@xmu.edu.cn）

六、报名

1. 网上报名，请扫描简章下方的二维码登录报名（需上传签字盖章后的附件申请表）。

2. 报名截止日期为2026年5月6日，录取结果将通过邮件的方式通知学员。

 3. 学员在厦期间，需遵守相关规定与考勤制度，防范各类风险，严禁下海游泳。