degreePolynomial -- computes the degree polynomial of a poset

Synopsis

Usage:

z = degreePolynomial P
Inputs:
- P, an instance of the type Poset,
Outputs:
- z, a ring element, the degree polynomial of $P$

Description

The degree polynomial of $P$ is the sum over elements $v$ of $x^{\operatorname{in}(v)} y^{\operatorname{out}(v)}$, when the exponents are the incoming and outgoing valences of $v$ in the Hasse diagram.

This polynomial is multiplicative for Cartesian product of posets.

i1 : B = booleanLattice 3;

i2 : z = factor degreePolynomial B

            3
o2 = (x + y)

o2 : Expression of class Product

Ways to use degreePolynomial :

degreePolynomial(Poset)

For the programmer

The object degreePolynomial is a method function.