Department of Mathematics and Philosophy

Undergraduate Research-Math 444

YangName: Mei Yang

Areas of Interest: Algebra and Combinatorics

Description: For students who have taken the introductory combinatorics course and learned the basic enumeration techniques and graph theory, there are many directions you may further explore. Here are a few suggestions:

(1) Compare advantages and disadvantages of different techniques by solving problems using more than one method.

(2) Investigate the relationships among different techniques. For instance, how to get generating functions from recurrence relations, or vice versa.

(3) You may further study the generating function method, which nowadays is the main language of enumerative combinatorics. Topics range from compositions of generating functions, generating functions in several variables, and application of generating functions to enumeration of trees, and various kinds of graphs.