Problem of the Week
Math Club
BUGCAT 2020
Zassenhaus Conference
Hilton Memorial Lecture
BingAWM
The chromatic polynomial of a graph, evaluated at positive integers, counts proper colorings of the graph. Richard Stanley proved that the evaluation at negative integers also counts something, specifically, compatible pairs of colorings and acyclic orientations. In particular, the evaluation at −1 counts acyclic orientations. I will present this influential theorem and its proof, as well as some consequences.