coxeterPolynomial -- computes the Coxeter polynomial of a poset

Synopsis

Usage:

z = coxeterPolynomial P

z = coxeterPolynomial(P, VariableName => symbol)
Inputs:
- P, an instance of the type Poset,
Optional inputs:
- VariableName => a symbol, default value t
Outputs:
- z, a ring element, the Coxeter polynomial of $P$

Description

The Coxeter polynomial of $P$ is the characteristic polynomial of the Coxeter transformation matrix $ -M M^{-t}$, where $M$ is the relation matrix. This depends only on the derived category of modules over the incidence algebra.

i1 : B = booleanLattice 3;

i2 : z = coxeterPolynomial B

      8    7    6     5     4     3    2
o2 = t  + t  + t  - 2t  - 2t  - 2t  + t  + t + 1

o2 : ZZ[t]

Ways to use coxeterPolynomial :

coxeterPolynomial(Poset)

For the programmer

The object coxeterPolynomial is a method function with options.