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Posets :: degreePolynomial

degreePolynomial -- computes the degree polynomial of a poset



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

o2 = (x + y)

o2 : Expression of class Product

Ways to use degreePolynomial :

For the programmer

The object degreePolynomial is a method function.