**UM Math Graduate Students Seminar**

Ziqian Ding

* University of Miami *

**will present**

**Something of Catalan Numbers**

Friday, April 10, 2015, 3:30pm

Ungar Building Room 402

**Abstract: **

In combinatorics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems. They first arise in tree enumeration problems of the type: "In how many ways can a regular n-gon be divided into n-2 triangles if different orientations are counted separately? In this talk, we will see some basic properties and give several interpretations of the Catalan numbers. We will also see some bijections between Dyck paths and non-crossing partitions. For the last part, we will step a little further into q-Catalan numbers.

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