z = zetaPolynomial P
z = zetaPolynomial(P, VariableName => symbol)
The zeta polynomial of $P$ is the polynomial $z$ such that for every $i > 1$, $z(i)$ is the number of weakly increasing chains of $i1$ vertices in $P$.
The zeta polynomial of the $n$ booleanLattice is $q^n$.


Thus, $z(2)$ is the number of vertices of $P$, and $z(3)$ is the number of total relations in $P$.


The object zetaPolynomial is a method function with options.