## Discrete Math Seminar: Samantha Dahlberg

- Date: 10/10/2017
- Time: 17:00

University of British Columbia

Chromatic symmetric functions and e-positivity

Richard Stanley introduced the chromatic symmetric function X_G of a simple graph G, which is the sum of all possible proper colorings with colors {1,2,3,...} coded as monomials in commuting variables. These formal power series are symmetric functions and generalize the chromatic polynomial. Soojin Cho and Stephanie van Willigenburg found that, given a sequence of connected graphs G_1,G_2,... where G_i has i vertices, { X_{G_i} } forms a basis for the algebra of symmetric functions. This provides a multitude of new bases since they also discovered that only the sequence of complete graphs provides a basis that is equivalent to a classical basis, namely the elementary symmetric functions. This talk will discuss new results on chromatic symmetric functions using these new and old bases, and additionally we will also resolve Stanley's e-Positivity of Claw-Contractible-Free Graphs. This is joint work with Angele Hamel and Stephanie van Willigenburg.

Location: ESB 4127

Tue 10 Oct 2017, 5:00pm-6:00pm