Combinatorics seminar
Combinatorics Seminar  Spring 2015
Tuesday 12.45pm1.45pm in room 226.
The Combinatorics Seminar is an introductory seminar for combinatorics. The talk should be accesible to first year graduate students.

Tuesday February 24
Speaker: Jordan Tirrell
Title: Counting flawed Motzkin paths by Motzkin paths
Abstract:
We'll look at paths which start and end at zero and take up, down and flat steps. These are called Motzkin paths if they contain no flaws, or steps below zero. Otherwise we call them flawed Motzkin paths. Eu, Liu, and Yeh showed in 2002 that the number of flawed Motzkin paths with a fixed number of flaws can be enumerated as an alternating linear combination of Motzkin numbers. We give a combinatorial interpretation of this result.

Tuesday March 3
Speaker: Olivier Bernardi
Title: Regions in hyperplane arrangements and trees
Abstract: A hyperplane arrangement (of dimension n) is a collection of hyperplanes (in R^n). The hyperplanes cut the space R^n in a certain number of regions (the connected components of the complement of the hyperplanes).
Given a finite set S of integers, we consider the hyperplane arrangement A(S,n) in R^n with hyperplanes x_ix_j=s for all i< j and all s in S. For instance, for S={0} the hyperplanes are x_i=x_j for all i,j, and the number of regions is n!. It has been noticed (in particular by Ira Gessel) that for many sets S, the number of regions of A(S,n) is equal to the number of labeled trees in a certain family. I will try to explain why it is the case.

Tuesday March 10
Speaker: Jordan Awan
Title: TBA
Abstract: TBA

Tuesday March 17
Speaker: Ira Gessel
Title: TBA
Abstract: TBA

Tuesday March 24
Speaker: Yan Zhuang
Title: TBA
Abstract: TBA
Previous semesters:
Fall 2014,
Spring 2014,
Fall 2013.