### q-Chromatic Polynomials

- Series
- Algebra Seminar
- Time
- Monday, April 1, 2024 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Andrés R. Vindas Meléndez – University of California, Berkeley

Via work of Chapoton (2016) on $q$-Ehrhart polynomials, $\chi_G^\lambda(q,n)$ turns out to be a polynomial in the $q$-integer $[n]_q$, with coefficients that are rational functions in $q$.

Additionally, we prove structural results for $\chi_G^\lambda(q,n)$ and exhibit connections to neighboring concepts, e.g., chromatic symmetric functions and the arithmetic of order polytopes.

We offer a strengthened version of Stanley's conjecture that the chromatic symmetric function distinguishes trees, which leads to an analogue of $P$-partitions for graphs.