#### Room 326

#### Chromatic polynomials and heaps of pieces

#### Bishal Deb

##### CMI

*Stanley in 1973 proved that the number of acyclic orientations of*

an undirected graph is the value of its chromatic polynomial at (-1) upto

sign. In this paper, he also defined a generalised version of the chromatic

polynomial and related it to the chromatic polynomial. In 1983 Greene and

Zaslavsky showed that the number of acyclic orientations of an undirected

graph with a unique sink at a fixed vertex is same as the coefficient of the

linear term of the chromatic polynomial of the graph upto sign. In this talk

we look at an involution on layer factorisations of heaps which we shall

use to prove the theorems of Stanley. We will also see how modifications to

this involution can be used to prove the result of Greene and Zaslavsky.

Done