Logo

Mathematical Sciences Research Institute

Home » MSRI-UP » Schedules » Chromatic Symmetric Functions of Trees and Unicycles

Chromatic Symmetric Functions of Trees and Unicycles

MSRI-UP 2013: Algebraic Combinatorics June 15, 2013 - July 28, 2013

July 26, 2013 (02:00 PM PDT - 02:45 PM PDT)
Speaker(s): Damien Gonzales (University of California, Berkeley), Arman Green (Morehouse College), Caprice Stanley (George Washington University)
Location: MSRI: Simons Auditorium
Video

Abstract

Given any simple graph, there is a corresponding symmetric function called the chromatic symmetric function (CSF). Introduced by Richard Stanley in 1995, the CSF of a graph G = (V(G), E(G)) is defined as follows:

XG=∑κvV(G)xκ(v)

where the sum is over all proper colorings κ of G. A proper coloring is a labeling of a graph such that no two adjacent vertices have the same label. In Geoffrey Scott's senior thesis, published in 2008, several open problems in graph theory were presented. In our poster, we investigate these open problems and generalize some of his results. Our goal is to find necessary conditions for any two graphs that will ensure that they have the same CSF. We first consider two special types of graphs: trees and unicycles and write a program in SAGE to compare the CSF for any simple graph, and thus, compile a library of graphs with a small number of vertices alongside their CSFs.

Supplements No Notes/Supplements Uploaded
Video/Audio Files

v1102

H.264 Video v1102.m4v 140 MB video/mp4 rtsp://videos.msri.org/data/000/017/327/original/v1102.m4v Download
Quicktime v1102.mov 198 MB video/quicktime rtsp://videos.msri.org/data/000/017/328/original/v1102.mov Download
Buy the DVD

If none of the options work for you, you can always buy the DVD of this lecture. The videos are sold at cost for $20USD (shipping included). Please Click Here to send an email to MSRI to purchase the DVD.

See more of our Streaming videos on our main VMath - Streaming Video page.