Title of the course: Combinatorial Counting
Instructor: Asst. Prof. Zafeirakis Zafeirakopoulos
Institution: Gebze Technical University
Dates: 14-27 August 2017
Prerequisites: Very basic knowledge of group theory.
Level: Graduate, advanced undergraduate, beginning undergraduate
Abstract: The course will span 2 weeks. The first week we study basic principles of combinatorial counting,
such as counting combinations with or without repetition, enumerating subsets etc. We proceed with counting trees,
labeled and unlabeled. Finally, we will count under symmetry using Polya theory.
The second week we will count combinatorial objects using geometry and generating functions. We will count integer
partitions under restrictions, network flows, linear extensions of posets etc.
The two weeks are independent, but together they make a good introduction to combinatorial counting. Especially for
beginning undergraduate students, it is recommended to start the first week.
Textbook or/and course webpage: http://zaf.zafeirakopoulos.info/nmk (The material will appear in a later date.)