**UM Math Graduate Students Seminar**

Ziqian Ding

* University of Miami *

**will present**

**Symmetric Group and Noncrossing Partition**

Friday, November 14, 2014, 2:30pm

Ungar Building Room 402

**Abstract: **

The symmetric group Sn with its cycle notation and the idea of a Cayley graph will be discussed in the beginning. After that we will show two different generating sets for Sn. Based on this, we will define two important orders: weak order and absolute order. In the second half of the talk, we will introduce the idea of noncrossing partitions and prove a very important bijection between the maximal interval in absolute order of Sn and the noncrossing partition of n.

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