Seminar Details
t-Core Partitions
- Start Date: February 8, 2017
- Event Start Time: 12:10 PM
- Event End Time: 1:00 PM
- Seminar Series: Graduate Combinatorics Seminar
- Presenter(s): Bryan Ek - Rutgers University
- Event Location: Mathematics Graduate Student Lounge -- 7th Floor | Rutgers University | Hill Center | Mathematics Department
- Presentation Type: Stand Alone Presentation
- Abstract:
The hook lengths of a partition are defined using the Ferrer’s diagram of a partition. Fix a positive integer t. If a partition has no hook lengths that are multiples of t, then we say the partition is a t-core partition. Let ct(n) denote the number of t-core partitions of n. I will give an introduction to the generating series of ct(n) and how we can use it to prove ct(n)>0 for certain cases of t. Dependent on time, I will discuss the existence of special t-core partitions with extra restrictions. This will mainly be a combinatorics talk that utilizes results in number theory.